Airbnb
Best for vacation rentals and homesharing, especially in urban cities
If you were to only search one place for a vacation rental, it'd be Airbnb. They went from selling Obama cereal to get more users to their status today as the preeminent vacation rentals marketplace with the most listings in the most cities. To top it all off, their design is top notch.
HomeAway
Great for whole home vacation rentals, especially in resort style areas
HomeAway (and its twin VRBO) actually started before Airbnb, but Airbnb came and sprinted past it reeeal fast. They've been trying to catch up ever since. Despite being smaller, HomeAway is still worth checking out. Their 1.3 million listings are nothing to scoff at and they're often better than Airbnb in resort style areas like Myrtle Beach since they bought regional focused marketplaces to build up to what they are today. They also focus more on whole homes instead of private/shared rooms, which may suit group trips better.
Tripping.com
Search major vacation rental marketplaces altogether besides Airbnb
Tripping.com searches dozens of vacation rental marketplaces, including HomeAway, all at once to provide you a better at a glance view. There's a lot of overlap between the ones they search and the listings generally aren't going to be much better than what you find on Airbnb and HomeAway, but it's worth checking if you really want to cover your bases.