Not bunching up is your best option if you don't want magic resist. Have your tank run in head on and then have your group split into two small groups that attack on each side bringing down the closest threat to them. If you can pull it off the Pincer attack is very effective even in non AoE fights.

I'd also go with displacement skills--Alistair, Blitzcrank, Singed, and to a degree--Shen. (If you can flank with Shen, Dash out to pick up a few people, then you can drag them from their position into your friends.
Also, Stand United on a DPS = sure death for at least 2 or 3 people on their team.

@juic3d
The best way to suppress them is to tell them. Then they will be mad for not having figuring it out themselves, and they will try their best not to use your tactic.

I bet the op had a team with 5 DPS

The simplest solution, just keep some distance or be able to split up in situations where amumu can jump in and ult or a fiddle ulti. If only one or two teamates get trapped in the epic AOE maddness the rest of your team should be able to focus down or push back the AOE'ers. Not to mention cleanse and the new cleanse item can help out.

Heavy scouting, vision warding, can avoid having your team trapped in an AOE ganks and usually turn all ganks around. Just realize each character has its unique means of avoiding and riot does a pretty good job of balancing the abilities out.

Stuns>AOE and can stop certain characters from initiating AOEs and can help focus down enemies

Team composition, if you have a lot of squisy casters/dps and 1 tank you will have the problem of being mowed down by stronger AOE mages. A balanced team should be able to hold its own against an AOE group. Even 2 or 3 tanks can't hurt.

AE Teams are really really nasty if they are correctly setup.

Yesterday i faced : Amumu + Morgana + Pirate + Karthus + Rammus
Horribly scary if you play Ashe or Heimdinger

Purge or Flash are probably the only way out of an "AE Situation".
Resists are useless unless you are tank (you'll die in 1.2 seconds instead of 0.8)

Janna.

Wait for Riot to nerf the composition.

The thing about AoE teams is that they're -really really- good at team fighting. It's kinda what the whole concepts designed for. Generally speaking though they're pretty bad at a number of other things. Pushing for example most aren't very good at. Don't get me wrong they're not the worst pushing team comp. in the game but it's pretty bad. They're also generally not very good at responding to/dealing with ganks.

AoE teams can be countered fairly well by early game ganking (ie: before those AoE's get nuts) which will give you a nice advantage.

AoE teams are also -very- countered by a solid 4 core with a dedicated offlane pusher. Even moreso if that pusher can handle themselves in a fight 1 on 1.

AoE teams work amazing when working as a group, if you can break up that group the strategy starts to get worse and worse. While defenses like MR work very nicely ultimately your best bet is to make them play on your terms not theirs. The longer you stick to the "Okay, 5v5 fight now" mentality the better off they are. Try a backdooring champ like Yi or Shaco; 10 bucks says that AoE team starts to complain about how "unfair" backdooring is.