Here are some of the ones I've heard of. All are last years. The program directors told me directly for the first two.
1. RIT Imaging REU had 240 applicants for 6 spots (I think these 6 were the first round of offers, though, there might have been more)
2. UMass Amherst Computer Science had 140 applicants for 9 spots, but they were able to fund an additional 8 or 9 through outside support, so there were actually a lot of opportunities there.
And in addition,
3. Bard College math now has a twitter account where they're letting us know how many applicants there are. They have 190 a week before the deadline, for 10 spots.
4. UPenn GRASP last year had over 80 for 10 spots, but that was their first year, so the number of applicants will likely increase.