We had a forum post about villain sidekicks that is pretty fun for raising the difficulty of vilains, you can see it Here.
As for hero sidekicks I've tinkered with the idea, it makes a great tool for houseruling heroes to play a bit different, and make some more powerful than they are now. All of the power's are for the hero they are sidekicks for. One of the trade off's we made was their incaps are negatives, varying by hero and how much they could use a boost.
Legacy:
Thiago 10hp
At the End of your turn, you may discard one card, if you do take an ongoing card from your trash and put it into your hand, or draw a card.
Power: Legacy deals himself up to 4 radiant damage, Thiago regains X HP where X = the amount of Radiant damage dealt to Legacy this way.
Incap:
Legacy must skip either his play, power or draw phase each turn.
I like it for the whole keeping Thiago alive routine, which hampers Legacy, but the ongoing recovery/deck burn really helps Legacy be a beast. It happens at the end because otherwise you could Take Down every turn. Another idea is at the start of the turn you can pull a one-shot from the trash, that makes him a pretty powerful damage dealer, but fits less with his normal play. The incap makes it key to keep Thiago alive, makes for an interesting challenge/bonus.
Bunker:
Sparky the field mechanic. 12hp
At the start of your turn you may destroy one of your equipment/ongoing cards, if you do you may search your deck or trash for the same type of card and put it in your hand.
Power: Bunker deals himself 2 irreducible melee damage, if Bunker takes damage this way you may play a card, even if another card says you cannot.
Incap:
When one of Bunker's Equipment cards is destroyed Bunker deals himself 1 melee damage.
Let's Bunker search his deck for an equip, basically to get any specific mode, equip, or ammo drop from your deck into play it costs you 2 card plays. The power gives you a way to upgrade while in turret or Recharge mode, melee damage seemed appropriate for Bunker's suit dealing itself damage. Could also do lightning if desired.
Unity: The idea here is that maybe Unity built herself as a bot to assist her in building golems, and that it becomes Golem Unity in the future. It is a little bit overpowered. (maybe not so little)
MakerBot: 12hp Golem
At the start of your turn you may destroy one Golem in play, if you do you may play a card.
Power: Take one golem from the trash into your hand.
Incap:
At the end of her turn Unity deals each Golem in play 1 irreducible lightning damage.
Originally we had her take the Golem back to her hand to play a card and that was way too powerful, as you could cycle out low health Golems for fresh ones, and put the other right in play again. This way it slows that down. Another option is to have you deal a certain amount of damage to a golem (probably 4) to play a card, that would split the diference pretty well, and give Turret, Champion, Swift and Cryo Bot a lot more value.
Tachyon:
Devra Caspit, Lab assistant: 12hp
At the start of your turn shuffle your trash and select a random card, put that card in your hand then discard a card.
Power: Draw a Card, Play a card. Tachyon deals herself 1 melee damage.
Incap:
At the start of your turn you must take 2 psychic damage or discard a card.
This really speeds up Tachyon, letting you take cards from your trash and discard worse cards, or at the least discard the one you selected from the trash, the power lets you burn your deck faster than your base power, and the extra card play can be really useful. The idea is not that Unity is helping you, but that your lab assistant is helping you. I assume Unity didn't have the best control over her powers at this point, and I wanted it to be more about Tachyon doing her thing, just more of it; instead of focusing on Unity's powers.
We also experimented with "Scenario Cards" that give a hero a specific upgrade for that match. These we were using by giving the villain a scenario boost and then shuffling the scenario cards for heroes and dealing one out, that hero being the "main" hero for that fight, I lost my stack of cards, but I remember some of them.
Bunker: Upgraded Interface; At the start of your turn you may return a mode card from play to your hand, if you do you may play a mode card now. (this is a recent addition, it's my favorite house rule for a boosted Bunker)
Mr. Fixer: Master of Combat; Form and Tool cards leave play by their own text at the end of the turn instead of when a card enters play. (this lets you have an extra tool or style card in play for your power phase, but ended up not being as fun as you'd think.)
Absolute Zero: Self Destruction Interface: Power: Destroy one of your cards, if you do AZ deals himself 4 fire or cold damage. (intended to make use of AZ's module insanity, letting you destroy them to heal or deal damage)