Now there are many vacation rental options and more people are dipping their toes in. My friend regularly lists her Santa Monica apartment (with cat) on airbnb.com. Or you can stay in a Snow Dome outside of Moscow.
You can also visit boutique-homes.com and find anything from expansive villas in the south of France to this vintage airstream rental in Big Sur.
London even has it's own site, onefinestay.com, that allows you to "live like a local" in a place like this Clarendon Road apartment. I also like this site because you can get a peek into all the impeccably decorated homes without the slightest intention of visiting London.
Do you prefer to stay in a hotel with all the amenities or live like a local in a vacation rental?