ESPN the Magazine had a great breakdown of the Major League batting average by count.  Here it is:

0-0: .262
1-0: .278
2-0: .293
3-0: .288
0-1: .232
1-1: .246
2-1: .263
3-1: .286
0-2: .174
1-2: .186
2-2: .203
3-2: .233

Notes:

1.) Batters hit the best with a 2-0 count.
2.) On base perctange is highest with a 3-0 count, which is expected (.757).
3.) Pike County native Mark Reynolds tied for the League lead with 7 homeruns hit while on full counts.

~ Jeff Archer