This is actually kinda hard as I like to play many different factions and in leagues where they try to force you to use all the mechs available to that faction, however I will try to come up with a lance and star for each weight that I would not want to use, hope that's okay.
IS
Light Lance:
Hornet - only redeeming quality to me is the low bv, but the relatively low speed, light weapons and thin armor even for a light make me avoid this even when playing FS
Garm - decidedly underwhelmed by this Mech, hope its not too new to include in this
Anubis - the only one I like is the experimental version
Osiris - 8/12/4 is very annoying movement, the 4D has 8/12/8 but its just too high BV for me to want to use.
Medium Lance:
Vulcan - I am not a fan of Vulcans, in 3025 or later they just annoy me
Whitworth - name should be Whitworthless
Cicada - Never been impressed by this, give me two locusts or a talon, I rarely play FWL though so...
Wolf Trap - I only include this to have a 4th Medium (I can usually find a use for just about every medium) I don't hate it, just don't like it very much
Heavy Lance:
JagerMech - some of the JagerMech IIIs are okay but this mech tends to die early and often on me
Rakshasa - the newest variant (Plasma and MMLs I think) is pretty cool but the original is painfully over BVed and dies too easily
Falconer - great mech if you're not using BV and only using tonnage to balance drops, otherwise painfully over BVed even worse than the Rakasha
Rifleman - I might take some flack for this but besides the one with two LBX10s that goes 5/8 I never liked the Rifleman (the clan version is okay but that's just because it pulses)
Assault
Charger - how can you not include this, hate it sorry
Banshee - also very under-impressed by this Mech, some of the later variants are okay though
Goliath - never had much luck with this, although I've seen it used well
Fafnir - again might be too new but while I can see how this is an awesome mechs, my inability to make piloting rolls (seriously I'll hit 12s on weapons to hit rolls before I make a 5 or 6 piloting roll) means I fall down every 2nd-3rd shot with the Heavy Gauss even while taking no damage. Basically any mech with a Heavy Gauss is something I try to avoid.
Clan
Light Star
Fire Falcon - never found anything this could do that another clan mech like the Kit Fox, Adder, Ice Ferret, Fire Moth, etc. can't do better - I will use them and be damn glad versus some other mechs but still not my favorite.
Mandrill - don't get me wrong, dual LRM20s on a light is nice even for the clans but there's an Adder variant for it.
Arctic Cheetah - way over BVed for what you get imo
Mist Lynx - standard jump jets on an omni (and 6 when there should be 7 no less) make me not like this 'Mech
UrbanMech IIC - meh, urbies are great in hoards in the IS - not what I want to use or see in the clans
Medium Star
Black Lanner - horribly over BVed mainly because of the masc. Drop the masc and I'd love this mech (though I generally don't like Masc on principle)
Shadow Cat - again the Masc (and Jumpjets) make this mech virtually worthless to me compared to other mechs on a BV scale
Griffin IIC - about the only IIC that I'd rather have the IS equivalent of sometimes
Huntsman - 50 tonner with the BV of a heavy? Standard jumpjets on an omn? weapon loadouts that garner even higher BVs? no thank you
Puncer - again standard jumpships (and 5 when there should be 6) make this over BVed and its relatively thin armor is annoying
Heavy Star
Ebon Jaguar - never liked the randomness of the weapons on this mech, it has its uses sometimes though
Hellbringer - paper thin armor and all its focus on randomnly chosen weapons can work sometimes in a zell fight but as those are less and less
Rifleman IIC 2 - the original is great (its actually pretty cheesy and I try to avoid it unless I'm fighting someone I don't like) but this one does a total of 8 damage - if all the UAC 2s hit with both their shots. Bleh.
Summoner - never liked the summoner much, its okay but the jumpjets make it high bv (again I hate standard jumpjets on an omni - jump jets are good sometimes but if they aren't needed I want configs without them)
Hellfire - meh masc
Assault Star
Phoenix Hawk IIC: Under gunned for a Clan Assault, new unjammable UAC rules that most places I play at make this a bit better but still underwheming
Gargoyle: 2 LBX 5s and 2 SRM 6s may have been enough in 3050 when just being a 5/8 assault was awesome but that doesn't cut it with me, some of the other variants are okay though
Bane: Lots of UAC 2s don't do much damage and jam a lot, better with unjammable UACs but still not a favorite. Love the Bane 3 though good lord.
Executioner: Masc!!! I hate it. But then again this is probably one of its best uses in the clans so...
Naga: Just for the sake of completeness I'll include the Naga because I don't like arty in the game at all but its actually pretty good at what it does.
Going over my list I'd like to note that a lot of these 'Mechs aren't bad at all - there are simply lots of others I would use before them.
Assaults- Charger, Imp, Shogun, Annihilator, gunslinger, natitana, Albatross
Heavies- Jagermech, Axman, Caesar, Rakshasa, Thunder, Daikyu, Anvil
Medium- Hoplite, Snake, Grim Reaper, Scorpion, Blackjack, Wolf Trap, Whitworth, Vulcan
Lights Ostscout, Hermes, Firefly, Hornet, Flea, Thorn
The bolded I agree with, others I can probably find uses for. The Naginata is the best C3 master the Dracs have for instance.