When I applied back in the day (a year ago!), I was originally going to apply to 15 programs, but then panicked when I saw everyone on this forum applying to 20 some places. I ended up doing the same, which was way to many programs. But I think why not, if you can afford it, apply to 15-20, better to be safe!
I think the odds of not matching are very slim for US seniors. Like 95% (I can't remember the exact figure) matched last year.
For me I picked a couple of top tiers, a couple of middle tiers, and a couple of low tiers. And ended up interviewing with the same strategy in mind.