There isn't a single hotel-casino on the Strip that provides childcare facilities for its guests -- not even Circus Circus -- although we know that the Venetian and MGM Grand, for example, provide on-site childcare for employees (the latter being open to all MGM Mirage staff).
When Bellagio first opened it had a no-kids rule, but the policy proved short-lived and the children of both guests and visitors are now allowed on property. Likewise, Wynn Las Vegas has a no-strollers rule, which we have seen both enforced and ignored, so you take your chances there. On the whole, we'd suggest that the Las Vegas Strip simply isn't a great vacation choice if you have young kids -- we recall a top executive at the Las Vegas Hilton some years back, when Vegas was still flirting with the "family destination" concept, commenting candidly that every time he'd ever seen a young child here, they'd been crying. And who can blame them? It's crowded, the casinos are huge and tiring to walk around, and there are so many places you can't go and things that you can't do if you're a small child.
In the summer, when you can hang out poolside all day, it's a lot more more kid-friendly (if the proposed new "Wet" waterpark and resort makes it off the drawing board, it will become even more so - see QoD 11/4/2006), and it's not as if there aren't plenty of options to keep older kids entertained (just check out our "Activities" section under "Vegas Info" for a whole bunch of ideas), but the city no longer actively encourages parents to bring their children, or at least not the younger ones.
All that said, sometimes there's no choice but to bring the little ones with you and mom and dad will undoubtedy need a romantic night off from the rigors of rollercoasters, M&M World, and FAO Schwartz. Or you may just be passing through and want a chance to explore the nightlife, in case you don't ever make it back this way. And, of course, there are going on a couple of million residents these days, who definitely need a night off once in a while and want to enjoy a bargain buffet, or celebrate an anniversary in style, or just catch a movie. In recognition of that fact, the parents in this latter group are much better catered to by the so-called "local" casinos (of which the closest to the Strip would be the Palms), many of which do provide on-site childcare facilities.
In our past experience, it's a pretty good service that we were very comfortable using and which our kids actually looked forward to, but it's been a while since anyone at Huntington Press had children of a suitable age (all being either too old or too young right now). While out filming for the Ultimate Blackjack Tour at the former Hyatt (now Loews) at Lake Las Vegas last year, a friend of ours did take advantage of their childcare facility and was very happy with it, but that's the only one we've heard about lately.
This is a question that we get asked on a frequent basis, however, so we'll present the facts in the table that this answer links to, but we'd love to hear from readers, whether you're local or visiting, with your experiences, positive or otherwise, of the facilities listed. Click on this link for a list of all the casinos that offer childcare, including their hours of operation, fees, and other information.