This post isn't so much a how-to on starting seeds, but some ideas on the types of containers you can consider. I'm a big fan of re-using and re-purposing, so I have a few suggestions for you!
1. Egg shells. When you crack your eggs for breakfast or for whatever recipe, try to break the shell close to the pointed end. Rinse the larger part of the shell and set aside for later planting. Bonus - egg shells provide lots of calcium for the soil as they break down.
2. Egg cartons. The cardboard kind, not styrofoam. Remove the lid and add soil to the individual compartments. Once the seedlings are ready to transplant to the garden, cut or tear the sections apart.
3. Empty toilet paper rolls. Cut four slits approximately 1 inch, evenly spaced, on one end. Fold in the resulting four tabs to create a bottom. Add soil.
Of course you can also use things like empty yogurt or pudding containers. You will need to carefully remove seedlings from these containers to transplant, so it's a little more touchy, but the containers work great. Just try not to disturb the roots too much. Either gently squeeze the sides, while holding the seedling close to the soil and pulling gently (upside down), or use scissors or garden shears to cut the container away.
Especially if you are using biodegradable materials, you will need a tray of some sort to keep the surface underneath the pots dry and clean. Purchased kits will come with a covered tray, but have a look around and see what you have already. And old cake pan, or even foil pie trays work great. How about clamshell containers from the bakery? Built in cover to keep in the humidity! If you don't have anything to hand to keep your egg shell planters upright, check out your local dollar store. You should be able to find a variety of disposable foil trays and pans there for $1 - $2 each, or even less. I picked up a super, covered, foil casserole dish for $1.25! Having a cover over your seeds aids in keeping the soil moist and the temperature warm enough for germination. You can remove the cover once the seedlings are an inch or so tall. If your tray/pan/etc. doesn't have a clear lid, cover your seed containers with plastic wrap.
Do you start seeds indoors? What kids of containers have you used?