I would like to know everybodys opinion on which champs ultimate is the best in the game overall. Then which is best for team fights. Which is best for chasing? Which is best for escaping? But mostly overall in every aspect which champs ultimate is the best?

Karthus's ult is the best. There's a reason it has a massive cooldown. It deals over 3000 damage (end game, of course), spread across 5 heroes, anywhere on the map. Name one other skill that deals over 3000 damage. Veigar's ult is the only one that even has potential. Maybe Nasus Q, though I don't remember if that was capped or not.

bump

karthus does have a good ult indeed that is if the game gets that late if karth isn't getting gold he gets pretty useless except is wall of pain

You could say that of almost any hero in the game, though, so it's a moot point. You're asking for ultimates, not ultimates based on the amount of farm a hero has. If you want bare heroes and their ultimates, I'd say LeBlanc. Does so much damage to a non-itemed hero.

Amumu ult. Teamwide stun while he deals aoe damage across your team based on max hp % and sets up his team for undeniable success. Same token for morgana, although you can escape from the actual stun, making amumu's better.

Orianna's ult is pretty damn game-changing if she can even land it on half the enemy team. So is Amumu's.

Malhazars ult is awesome supressses enemy adc. Pantheons ult is good to pop in in a team fight. Veigars ult combined with his Q two hits squishes and totaly takes out 70% of some champs health given that he was lvld up his Q

I'm a big fan of big initiation potential from my ultimates, as opposed to just raw damage. Skarner's is absolutely devastating, to just be able to pick out the other team's AD carry and drag them into your team. I'd also rank Amumu, Sona and Galio up there for great AoE lockdown. Malphite and Hecarim have great counter-initiation ultimates that completely swing fights.

Best for team-fights: Amumu
Best for chasing: Hecarim
Best for escaping: Malphite
Best overall: Galio