Weedy waters can be a ton of fun. I had the chance to fish a typical MN lake-complete with a super weedy bottom and cattails galore-this last summer.
Here are some good ways to fish them:
Spinnerbaits: The ultimate weedless lure. These suckers can cut through the thickest weeds. You'll want something heavy to get down there, though.
Buzzbaits: The topwater equivalent of spinnerbaits.
Jigs: Not 100% weedless, but they get the job done. You can try flipping, pitching, punching, or just plain old casting.
Topwaters of any kind on top of any water that doesn't have weeds poking through. This would include frogs, which are totally weedless, and soft plastics like the Rage Toad or a floating worm.
Hope that helps.