After the recent QoD (6/23/2009) about the fact that not only will the Hard Rock not allow you to take booze or soft drinks up to your room, but not even a bag of pretzels or potato chips, we were not expecting a positive outcome to your question. How wrong we were!
We called to the front desk of the Flamingo and asked if we could order pizza delivery to our room. They said the pizza ordering part was fine, but that it couldn't be delivered direct to your room. The deliverer would need to go to the front desk and the hotel would call your room to let you know it was time to come down and pay for/collect your dinner.
As is our custom, we then tried a few other places to see what they said. Bellagio, when they finally answered the phone (grrrrr, we were on hold for an age) gave exactly the same response (which impressed us, considering that their in-room dining menu offers four types of pizza). Next stop, the Mirage, which was less accommodating. There, the pizza can't even be delivered to the front desk -- the deliverer has to call you and you can meet at either the main or north entrance. Still, the fact that you are allowed to order in, when they have the California Pizza Kitchen on the premises, surprised us. Boulder Station, which has a Metro pizza, was as helpful as the Flamingo (but if there's a Metro on property, we'd suggest there's no need to order in).
As to which companies will deliver, you should be fine with a big chain like Dominos. We like Villa Pizza and when we called their W. Sahara/Valley View location, they confirmed that they'd deliver to a Strip hotel, as long as you met the driver at valet. Metro Pizza, a great local chain, will also happily deliver and meet you at the front desk/concierge.