To further complicate things, Fighters and Scouts - to some degree, are fairly good against Seige & Colony ships too, since they all share light armor (& constructors too?!).  I also believe the structure killers (TEC Orgrovs & Advent starfish) carry light armor, so are suspectible as well.

Structure killers are only good against structures.  Siege are good for planet bombing only. 

Finally LRFs are fairly good against Cap ships as well. 

Oh, and then TEC scouts, can also be good against structures, if you research the teir 3 tech for timed explosives.  Also, additional research can improve LF's against the higher tech support ships, ie.: antimatter robbing/interupts etc..

EDIT: aww... Dorian was posting at the same time... so disregard.

Correct, LF get a damage modifier bonus (150%) to anything with Heavy Armor.

LOL. Is that a new type of dinosaur (spelling)?  But yeah.

I should have also mentioned, that HCs are good against pretty much everything, and supposely more so against LRFs.  But that doesn't currently seem to be the case against Illuminators.

They'll kill the carriers

Illums are bugged, and many people are getting fed up with it.  I've actually been seeing "no Advent" games popping up lately. 

Light frigates, in practice, are often treated as a counter to scouts.  They don't have any particular attack bonus against them, but their armour type gives them the ability to tank scouts with ease.  Flaks do get a damage bonus against scouts and their multiple weapon banks make them effective against swarms of light units like scouts. 

In practice, both LRF and heavies are very useful for killing carriers.  They aren't quite as good as light frigates, but their high DPS means they'll still get the job done quite efficiently.  If you can combo heavies with fighters (to reduce bomber presence) or LRF with flaks (to reduce fighter presence) you can actually counter carriers quite easily like this.

Long range frigates are, in practice, a counter to capital ships.  Their long range makes them idea for focus fire and they deal high damage and have a relatively good modifier against capital ships.

I could probably add: Scouts < LF (& Flak).  As Darvin mentions, LF, & Flak (to a lesser degree, I think), both do a pretty good job of countering scouts.  But what doesn't counter scouts?!  Besides LRF?  Bombers??  And...
I could probably add: HCs, SBs & Cap Ship > ALL.  Those three deal relatively high damage to all types (except strikecraft). 
Additionally, I noted that turrets get a bonus against Medium armor, so they damage LFs best.

So it would look like this:

                                                                LRF
                                 Flak     > (fighters) > Scouts   (< LF & Flak)
Scouts > LRF > LF > Carriers          | 
                               Support          v   
                                              (bombers) > HCs          > All
                                                                 SBs           > All
                    >                                           Cap Ships  > All
                                                                 Structures
                                                                 Turrets       > LF

Capital ships and starbases are not a counter for LRF from what I understand.. whether they should be made so is the subject of a current debate.

The relationship of support to LF and heavies is complicated as some support cruisers have abilities that counter short ranged weapons rather better than long ranged weapons.

Also LF are a very weak counter to scouts at best- scouts and LRF share the same armour type and LF are penalised against it, to allow LRF to have superiority.  Plus scouts can evade short ranged weapons as they have a speed advantage.  I've contended elsewhere that there are fundamental problems with the existing relationship of LF and LRF which have a negative impact on the entire game.  Basically LRF are both heavy-hitters and counters to fast agile LF, and might need to have one role removed.  Their weapons don't suffer a substantial penalty against any target.

Unfortunately the combat mechanics sticky hasn't been kept up-to-date, and we could really use another table.  This is a list of 1.1 and 1.8 balance changes only some of which are in the table, I may have missed some from the patches in-between:

AntiLight attack type's damage modifier vs CapitalShip, Medium, Heavy and VeryHeavy armor increased from 25% to 50%.
AntiVeryLight attack type's damage modifier vs CapitalShip, Medium, Heavy and VeryHeavy armor increased from 25% to 50%.
Composite attack type's damage modifier vs Medium armor increased from 100% to 125%.
Composite attack type's damage modifier vs Heavy armor decreased from 125% to 100%.
AntiHeavy attack type's damage modifier vs Heavy armor increased from 125% to 150%.

AntiMedium damage type's modifier vs. Medium armor reduced from 150% to 133%.
AntiVeryLight DamageType's modifier vs VeryLight armor reduced from 150% to 133%

Anything that isn't a colony frigate, siege frigate, or long range frigate, basically.  Scouts are countered by almost everything in the game simply because of their weak combat stats.  Their only saving grace is that long range frigates, the only combat unit they DO counter, are the backbone of combat fleets as we know them.

OK, here is a more complete list/diagram of all important types.  It might now be so crowded that it is hard to follow,  But it should be correct.   I didn't include hangers, superweapons etc. because I believe they all fall under the broad category of Structures. 

I don't know what mines are best against?  And I guess mine's attack varies by race.  Anyone know?  Maybe check the entity files?  And from what I understand, the combination of both scouts & flak actually work the best against mines. In any case, the scouts are needed to locate the mines.  For simplicity's sake I was tempted to leave off most of the Scout's counters, except for LRMs (& Mines), since the Scout's counter against LRFs is the most significant.  In other words, all the ships with light armor - all of those that fighters counter: Constructor, Colony, Siege, Torpedo. The scout it is unique in having the same armor and damage type - it has both light armor & light attack, so I guess it is also good against itself or other scouts.

           >                                                  >  Constructor
           >                                                  >  Colony
Scouts  >                                                  >  Siege         > Planet
           >                                                  >  Torpedo     > Structures & SBs
           >                                                  >  LRF
                               >  Flak     > (fighters) > Scouts   (<) LF & Flak
Scouts  >  LRF  >  LF > Carriers     /     | 
                               >  Support    \     v   
                                               (bombers) > HCs          > All
               LRF (>)                                      > Cap Ships  > All  (LRF less)
                                             >                 >  Star Bases > All  
Scouts  >                  Torpedo  >                 >  Structures
                                              >                 >  Turrets       > LF
Scouts  >  Mines   >  ?

Edit: Note that Fighters counter ALL of the ships directly behind and above the arrow.  Same for Bombers, they counter ALL those listed directy beyond and below the arrow.  (I added arrows for each, hopefully not adding other confusion).

The counters listed in parenthesis, for example: (>), or LRF countering Cap ships, are 'soft' counters, rather than a 'hard' counter - in which the damage type matches the armor, and recieves a damage bonus.  Carriers themselve don't have any weapons, or a specific attack, but they field strikecraft: either fighters or bomber, thus they are listed in parenthesis, as part of carriers (with slash lines connecting them to carriers).

DesConnor can you (or anyone) please explain your observation that "Capital ships and starbases are not a counter for LRF".  

Yeah, I agree.  I didn't mean to say that LRF were good against starbases.  I edited the diagram to help remove that perception.  I list Heavies (HCs) as being good against All.  I don't know if that is neccessarily correct, but they do have a "Composite" type of attack with a good modifier against all types.

Capital ships are not a counter for LRF as from the damage tables they only register 75% damage on them, and as the LRF have 75% of the own damage effective against capitals there's no advantage.  Why this should be I'm not sure. 

Capitals do 100% damage to LF and only take 50% in return, for comparison.  I would allow that LRF are more effective against starbases than LF, unless Darvin has an alternate approach to the damage table logic?  Even heavies take more damage from starbases.  I've watched as few as 6 LRF (LRM as well, not Illuminators) kill a starbase when they had a repair bay behind them. 

You could also add bombers against structures and starbases, thats a counter, even if Entrenchment has a few structure upgrades to allow them to fight back.  

Bombers, LRF, and heavies are capital ship counters.  Yeah, they only have a 75% modifier, and everything else is in the 25-50% range. Combined with the fact that these are your highest DPS dealers to begin with, and they really do mince up capital ships well.

I don't know where you're coming from here.  It's very obvious to anyone who has played the game that these three units are the most dangerous to capital ships.  In sufficient numbers, light frigates and fighters can be trouble for caps as well, but in the same numbers a swarm of LRF or heavies or bombers is going to slaughter those caps.

Capital ships don't really counter anything.  Unless they're a very high level, almost any type of units will beat them at an equal price-point.  They're about the special abilities.

Actually I didn't even look at the damage tables.  This is based on pure gameplay experience.  Heavies, light frigates, and long range frigates are all equally good fodder for charging a starbase.  The key to beating a starbase is to bring it down before it starts killing frigates.  That means you want to smash it with a large amount of DPS and try to hold it off with repair and defensive abilities.  For instance, I don't care whether I have destras, illums, or disciples; the key to smashing a starbase as Advent is sufficient antimatter on my Progen for shield restore and having guardians.

The bottom line is that whatever units you throw at a starbase in a direct charge are going to be at the mercy of a powerful array of guns.  The key to winning is to provide superior support.

Oh, give me a break.  The repair bay won this fight.  Would have been the same whether those units were light frigates or heavies.  Heck, this starbase was clearly immobile and unsupported (otherwise the first target for takedown would be the repair bay) so you could have easily just killed it with bombers.  That said, I'd have expected the repair bay to have run dry before such a small number of frigates managed to kill a starbase.

In the same sense that LRF can kill carriers before fighters pick them off, yes, this is true.  Doesn't change the fact that fighters still mince LRF and bombers still crush heavies.  It's all in the way they're used.

In theory you can kill a starbase with fighters and it cannot retaliate, but the whole point is that this will take positively forever compared with the much higher damage you get out of bombers. 

Who ever talked about capitals countering LRF?  I'm talking about LRF countering capitals and I thought you were too.  Capitals as direct attackers are a counter to nothing.  Any combat frigate will outperform them at an interception or takedown role unless you have a special ability to tilt things in your favour.  As for starbases, starbases have so many weapon banks that they're attacking pretty much everything within range.

Honestly, off the top of my head I don't even know what the relative modifiers each of these types of units get to starbases.  What I will say is that all three of these units are commonly used as fodder when swarming starbases, and are effectively used in the same manner.  While some may strictly speaking be better than others, at the end of the day they all fulfill this function and aren't categorically better or worse.