Two. Bally's and Tropicana.
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. It's just too much of a risk for any hotel to permit, especially in light of all the drunken shenanigans that tend to typify the "daylife" scene.
A great gallery of postcards shows 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; check 'em out.
Bally's Olympic-size Blu Pool has a 12-foot deep end and is open to non-hotel guests for a $10 fee.
The Tropicana's main pool is somewhere between five and six feet deep at the ends.