Nope, just the good old fashioned, freedom-loving single lever. I've seen the button one at restaurants and offices and whatnot, but never in someone's home. I have three toilets in my house, my parents have three, and my siblings each have two or three, and all of them use a single lever. Some of them have less water in the bowl, but all of them use the standard flushing mechanism.

It turns out water is pretty cheap even in my desert state (Utah), the city just does a good job cleaning it up for reuse (I think it goes to irrigation, not completely sure). So while we have incentives for reducing gardening water (especially lawns), electricity, and gas use, I haven't seen an incentive for those low-flow toilets for residential homes, probably because toilets aren't user of water (showers use a ton more).