Only nine (now ten) players have ever put up a batting average less than .30000 with over 200 hits in that season. When you trim that to a rounded off average of .300 or less, you can add a tenth (now eleventh). Here's the players:
Juan Pierre has the worst batting average of any of the players ever to do this, by a relatively wide margin. He's right in the middle of the pack for on-base percentage, however, which is unsurprising given how little you must walk to even get 667 AB in the first place. A player at every position except catcher (and they probably shouldn't count, since even the best don't play every game) has done it.
EDIT: Jimmy Rollins made the list for 2007 with 212 hits in 716 at bats, good for a .29609 average.