Alex and I long ago stopped microwaving anything plastic and recently have stopped washing any plastic in the dishwasher. While there is dispute about plastics and exposure to heat -- do they leach or not? -- we aren't taking any chances.
Most of the plastic we use is related to the boys, from sippy cups to plates to small storage containers. Chances are, many of the cheap plastic DO break down and release toxins when heated. Besides, they discolor and warp and sometimes they even smell funny. If you are curious about good and bad plastics, here's a decent guide.
We are gradually switching to all glass containers for food storage. This is not an inexpensive proposition, but I have to say it feels a bit luxurious to use pretty glass containers for our leftovers. I prefer the type you can use in the freezer, dishwasher, microwave, anywhere. Most have plastic lids, so we still have to hand-wash those, but I've found some with glass lids. I figure while I'm finding ones that work and aren't crazy expensive, I'll share the findings here. Please feel free to comment on your favorites.
Crate & Barrel "refrigerator dish" (this has a glass cover)
Crate & Barrel round set by Frigoverre (I have these and like them; other sizes available
Greenfeet.com also has a nice selection (and if you join, you get 10% all year long)
Pyrex is another good option, available through Amazon and others