Alright, I pulled these up with a LoL Replay of a Dominion game.
Bonuses Granted:
The character model grows by roughly x2
The first grants an absorption shield with 212.5 (+12.5 x level) health that will recharge if the champion doesn't receive damage after 10 seconds.
The second buff allows the champion to passively detonate a lightning blast inflicting 90 (10 x level) magic damage on the champion's autoattacks and damaging spells with a 4 second cooldown.
Spawn Time: 3:00 Minutes
Channel Time: 5 seconds
Respawn Time: 3:00 Minutes
Duration: ~45-60 Seconds (Not positive on this one, hard to find a game where someone kept it the whole time.)
Source: League of Legends Wikia
Riot games have put a special effort into having balanced champions for this game style as well. I don't believe there are any champions to avoid. However, the team composition changes a bit.
AP Carry
You will still need one, or else the other team will just build against AD and will own you as soon as they are a bit stuffed.
Tank / Off Tank
King in solo holding the bot lane, also very good in "tower diving" (if we can still call it so in Dominion).
Melee Fighters
They tend to be the heroes everyone picks as they are sort of kings on this map. They deal quite some damage and have high sustainability (so they don't need to Back often), and are often very good in 1v1 (which happens pretty often in Dominion).
Ranged AD Carry
More than one is too much, but not having one (to have more fighters) is a handicap. He deals crazy damage and can attack out of tower range or defend minion waves without exposing himself in front of the tower. From the games I've played or seen, having only melee champs is clearly a handicap.
Support
I rarely see them in Dominion and believe they are overlooked. Each time I've had one on my team, it was awesome to hold the windmill (we never had to back, support would always buff/heal us).
However, having a support requires good team play, because the champion won't do anything on its own (compared to fighters).
General
As XP gain is so fast in Dominion, teams are usually built with mid/late game champions. Riot tried to correct this in a previous patch by lowering the XP gain aura on the map, however, you still get to level 6 tremendously fast, so don't hesitate in taking weak early game champs (like Kassadin, useless before level 6).
Try having a hero or 2 (at least) with high mobility (Rammus, Kassadin, Nocturne, Twisted Fate, etc.) to do lane swaps and be unpredictable in your tower attacks.
Conclusion
All heroes are viable. It all depends on the team composition.
Good Akali, Irelia and Xin Zhao champions can however be freaking awesome with their ganking abilities and life steal.
Best Answer
Skills that work with teammates
Skills that do not work with teammates
Possible Skill Interactions (Untested)
Thresh's The Box damaging and enemy only once no matter how many different Thresh walls they break.
Vladimir's Hemoplague Either refreshing the duration or stacking for more increased damage.