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.
This is completely situational.
When I definitely win my lane, I leave their turret up so I can get more kills against them. O the other hand, if I'm losing the lane, I like to take the turret down ASAP.
Best Answer
Hmm, a misconception is that you have to have a teamfight. League of Legends allow you the flexibility to capture objectives without ever having to teamfight. A simplified case could be one team trying to baron, and the other team decides they can't contest baron so they push a lane hard. After baron, the team decides they lost too much to try defending, so they will go push a different lane themselves and it's a base race. No teamfights, no anything else.
Ultimately the laning phase ends when one team decides to group up (generally mid) and take a tower as an objective rather than going for dragon/baron. At that point they are saying, "We are not going to just farm the lane anymore. We want to push to your nexus. Try to stop us." The other team then has to decide to ignore it (generally ill-advised since a 5-man team at this point can easily tower dive, win a fight 5v4 or 5v3, then push as 5, while one champion is not going to be able to push as fast by themselves or even as a 2 man.
Getting objectives "phase" is always happening until one team won through surrender vote or the nexus is destroyed. Objectives in League of Legends can be broken down simply as: 1) Destroy enemy Nexus 2) Destroy enemy nexus towers 3) Destroy at least one enemy inhibitor 4) Destroy at least one enemy inhibitor tower 5) Destroy at least one middle tower 6) Destroy at least one outer tower 7) Gather gold and experience to help you accomplish the above objectives
This is the simplest and minimum requirement of the game. Ultimately you want to destroy the enemy nexus, however it has a prerequisite that the inhibitor must be destroyed and both nexus towers are destroyed. To destroy an inhibitor you first have to destroy the tower protecting that inhibitor, and so forth. Gold and experience are your resources to help you accomplish the objectives. Everything else, supports that as champion kills, CS, dragon, baron all does just that for you and your team.