I recently heard this idea for cucurbits (cukes, melons, squashes). Line a green plastic berry basket with newspaper and fill with soil. Add seeds. When it's time to plant, you just plant the whole thing into the garden. The newspaper will become compost, and the roots will grow through the holes in the berry basket. The advantage of doing this is that cucurbits don't like to have their roots disturbed. (I'm going to try it this year, planting both with and without the berry basket.) My gardens are a few miles away, so I like to start my cucurbits in a cold frame where I can keep an eye on them.

I used peat pots one year and didn't like them. They seemed to be too wet or too dry, and it was harder to know if the plant was getting the right amount of water. I've since heard that it's a good idea to tear off the top edge of peat pots when you plant so that it's not sticking above the soil line and wicking water away from the seedling.

Another alternative to peat pots (but not more cost effective!) is Cow Pots -- made out of composted manure and made to be planted in the ground where it slowly feeds the seedling, too.

And someone in my garden network makes flats from scrap lumber, with hardware cloth stapled to the base, lined with newspaper. Transplanting still involves some root disturbance: you're not pulling the seedlings out of a container, but rather scooping a handful of soil along with the seedling.