Vacation rentals, for instance, offer many amenities that the majority of hotels do not.  Usually owned by regular folks (renting a vacation home means helping a "mom and pop" business instead of a big corporate-owned hotel), vacation rentals tend to give you full kitchens and multiple bedrooms.  They're available everywhere you might wish to stay too.  You can find condominiums or houses (with detached homes you get the ultimate in privacy for your vacation) in any part of the world. 

If you prefer to be surrounded by the hubbub, you can find rentals in the middle of the action (perhaps a condo on the Las Vegas strip or a cabin with ski-in-ski-out convenience tickles your fancy), but you can also find rentals that cater to peace and quiet.  Many of these homes are set back from the busy streets and thoroughfares where hotels dominate (instead of a condo adjacent to Vegas casinos, maybe you'd prefer a house a few blocks away with a fenced yard and a private swimming pool).

What about families who travel with pets?  Is a hotel or a vacation rental more likely to accommodate them?  Well, I don't know about you, but I haven't seen too many hotels that appreciate even well-mannered dogs waltzing through their lobbies (even on a leash).  On the other hand, vacation rentals are often the way to go for pet owners, because many will accept dogs and cats (with an additional deposit).  Do make sure you check on the place's pet policy beforehand, though, since each owner sets his or her own rules.

The last thing I want to mention is the overall ambiance of vacation rentals versus hotels.  With hotels (especially big chains), you get... pretty much the same thing no matter which part of the world you visit.  This can be good for those who don't like change, but if you want to stay somewhere that embraces the culture of the local area, you're more likely to find that in a vacation rental.  Many owners stay at their properties a few weeks a year themselves, so the homes often feel like, well, homes.  They're cozier and friendlier than the starkness of most hotel rooms.

Lest you think I have an agenda for promoting rentals over hotels (alas, I own neither), I must admit that there are a few downsides to vacation rentals.  First off, finding just the right place can involve more internet research than simply booking through a web site that offers travel package deals.  Second, because vacation rentals are usually privately owned affairs, it can be hit or miss with service.  Not all rental owners have their own web sites, and it may take a while for the proprietors to get back to you if they don't use a management company.  Third, most vacation rentals don't come with housekeeping.  The premises will be clean when you arrive (in fact, you'll often be charged a cleaning fee), but don't expect anyone to come in and change your sheets every day.  Lastly, rentals tend to be more expensive than hotels.  You do usually get more square footage for your money (multiple bedrooms, full kitchen, separate living and dining rooms, etc.), but you pay for it.  That's why rentals are popular with families and friends who can share the costs.