Some thoughts on fighting rain teams:
Trick-Scarf leads like Uxie help a lot, since your opponent is only getting 5 turns of rain if he leads with Rain Dance, and none if he doesn't (many Electrode will lead with Taunt if you can't OHKO them). Many Rain supporters have a plan for getting their sweeper in without damage, such as Explosion, U-turn, and Lunar Dance, and Trick will stop them from doing these things, as well. Both Uxie and Froslass can use Trick and Thunder Wave, so they can easily Trick Electrode or Ambipom and then spam Thunder Wave until something comes in. Trick leads have a good chance of starting the match by crippling one supporter and one sweeper right off the bat. You can further cripple a sweeper by tricking them a Damp Rock, but this is usually only worth while if you intend to sacrifice your Trick user that turn.
Encore can work in a similar way to Trick, foiling the support pokemon's "exit strategy" and giving yourself a free turn to hurt the sweeper that he now has to just switch in on its own. This is especially great with Pokemon who can set up a Substitute as your opponent switches, such as Azumarill, Poliwrath, and Raichu. Encore is nice, but just having Substitute and the ability to cause a lot of damage can help against Rain teams. Pokemon like Rhyperior and Aggron can get their sub up against Registeel or Uxie and take out an enemy sweeper as they break the sub. Also keep in mind that any pokemon with Substitute can stall out half of the rain if you can get the sub up first.
This was touched on earlier, but bulky users of Thunder Wave are your friends. Uxie and Slowbro come to mind, as well as Chansey, Clefable, Cresselia, Lanturn, Porygon 2, and any Regis, to name some. Once you paralyze a sweeper, you can either revenge it or take advantage of it's paralysis or a possible switch to stall out the rain.
Those are just some ideas, a lot more have already been mentioned in the thread. Try to find a use for every teammate in a Rain situation - for instance, anything with Substitute or Thunder Wave is useful against Rain, period.
My main team looks like this:
Venasuar, Articuno, Hitmontop (spinner, not priority), Moltres, Rhyperior, Cloyster. That probably doesn't sound like a team that can stand against Rain all that well, but with some creativity I've managed to get it to work. Venasuar is obvious, as he can take hits from the Special sweepers and retaliate with Grass attacks or Sleep Powder. Articuno can wall special Ludicolo pretty comfortably with Roost and can usually wall the other Special Sweepers long enough for Rain to go away. Hitmontop basically can take 1 hit from something and retaliate with a Fighting attack, often dispatching Omastar and Kabutops. Moltres comes in on a supporter and Subs up. Depending on what happens next, he can Poison and stall a sweeper, or just stall out half of the Rain with Sub, with Toxic as a parting gift. Rhyperior is really useful, using Substitute against supporters and then pummeling the sweepers from behind it. Finally, Cloyster walls Qwilfish and Floatzel to Timbuktu and can even survive a Stone Edge from Kabutops at full health, and can retaliate back with boosted Surfs. This is meant to be an example of how you can beat Rain without going to extremes. As shaky as all of this sounds, I win against Rain more often than not. I'm not saying you can all suddenly decimate Rain without changing your teams, but give some thought to how each member of your team can play a role, no matter how small.
