The answer is "not many," and those few there are tend to be at the few surviving old-school establishments. For example, Binion's cool rooftop pool has seldom been used since the hotel closed a few years back, but it has an eight-feet deep end, dating back to when that tower was part of The Mint.
Any pools built from the mid-'90s onward have been officially limited to a maximum depth of 3'6" and there's no diving at any Las Vegas hotel pool these days -- high-diving boards, although common in the early days, were all phased out in the late '70s, with the rest of the regular boards pulled by the mid-'80s. We tested the water with the Trop in the course of researching this answer and the representative with whom we spoke could not have been more emphatic when he exclaimed, "Definitely NO DIVING! The lifeguards will kick you out!" It's just too much of a risk for any hotel to permit, not least in the light of all the drunken shenanigans that tend to typify the "daylife" scene (we've actually seen someone in a wheelchair pushed into a pool, albeit with their consent, so it was evidently a drunk person in a wheelchair. It wasn't so easy getting them, or the chair, out again...)
There's a great gallery of postcards, however, showing the high-diving boards back in the day at the Stardust, Desert Inn, Sands Frontier, Royal Nevada, Sans Souci, et al, courtesy of the Vintage Pool Party group on Flickr, so check 'em out.
And that's it for deep ends, to the best of our knowledge, outside of those public pools designed for diving.
Photo of Sands pool appears courtesy of Las Vegas News Bureau.