Going back to elementary school…
2 wins (300 meter run and 400 meter run, at city meets for my grade/age group)
Junior High
1 win (7th grade 800 meters; 2:40 - I recall the 1500 was pretty stacked at that meet, leaving the 800 wide open)
High School
1 JV XC win
4 Varsity XC wins
0 track wins (but plenty of second place finishes - stuck around 10:50 for 3200 most of the time, got down to 10:20ish for a few peak races)
College
0 XC wins
2 track wins + 1 track first in heat (none of these were my best times
1 half marathon
2 road 5ks
Post College
2 track wins + 1 track first in heat (again, generally not my PR's, although one was pretty close to mile PR with a win in 4:17)
6 road 5ks (that I can think of now - mostly in the 15:40-15:55 range)
1 15k win
So I guess it looks like about 20 times, depending on how you count it. I may have missed a race or two - also, it seems like a lot of my best races have put me in 2nd-6th place; it is pretty special when you can have a great race and also win!