I think it'd be fun to build a little mini-fantasy baseball game, but after a bit of Googling, I'm getting the impression that there's no easy and reasonably-priced (or free!) way to get that data. Have any of you done something like this? Should I be thinking about screen-scraping?
I would be wary of screen-scraping. The MLB is notorious for unauthorized use of their stats and players' names. That's why the prices are "out of the park" for you -- those places pay for a licensing fee to use the players names and stats.
Also, I found these:
I've used FanGraphics before to look up live stats... I'd imagine you could scrape the page fairly easily given its layout.
It turns out that MLB.com exposes a TON of data, but I'm not sure yet if it's updated in real-time. And some of the answers here so far are making me afraid of using it. :)
I wrote an library that lets you easily use the MLB real-time data. You can find it at: http://gameday.timothyfisher.com
FYI, while MLB can control access to the gd2.mlb.com server, their attempts to control usage of player names and stats were ruled against by the supreme court in a case a few years ago. Anyone can use stats and player names without obtaining a license from MLB.