Eric Seidman at Fangraphs has a nice article summarizing research on when sample sizes become (somewhat) reliable for hitters. The research suggests that the following stats begin to stabilize with the corresponding number of plate appearances:
50 PA: Swing %
100 PA: Contact Rate
150 PA: Strikeout Rate, Line Drive Rate, Pitches/PA
200 PA: Walk Rate, Groundball Rate, GB/FB
250 PA: Flyball Rate
300 PA: Home Run Rate, HR/FB
500 PA: OBP, SLG, OPS, 1B Rate, Popup Rate
550 PA: ISO
Did not stabilize by 650 PA (the cutoff): BA, BABIP
The underlying work was done by a well respected analyst who goes by the handle Pizza Cutter at the Statistically Speaking blog. His research on pitchers is here.