You have two basic options: On Disney Property of Off Disney Property.
I have personally done both, and both are good for different things.
On Disney Property:
-Use of Disney Amenities (airport shuttle, sending souvenirs bought in the parks to your hotel, Extra Magic Hours, etc.)
-Use of Disney Transportation between the parks (although this isn't a perfect system and can sometimes be time consuming).
-Wonderful theming; immerses you in the Disney experience.
-Use of Disney Dining Plan while at hotel.
Off Disney Property:
-[Sometimes] better rates.
-Larger, suite-like rooms (in some hotels), where Disney rooms typically hold only 4-5 people.
-Freedom to use your own vehicle, if you so choose.
There are obviously more pros and cons that I can list, but you get the general idea.
When my family (before I was married) went to Disney World the last time, we stayed at Caribe Royale, and it was great. The suites were very roomy, and we got a great rate. Mousesavers is one of the best resources for finding good hotel rates:
Go to Mousesavers.com
Click Walt Disney World in the left column.
Click Preferred Hotels near Disney World.
From there you can see Mousesavers' top picks for hotels near Disney World, and most (like Caribe Royale) offer a "Mousesavers rate" that you reference when booking. Mousesavers rates also vary by Disney's Seasons (discussed in this post), so it always pays to go in lower seasons.
If you're wanting the total Disney experience, you can't beat Disney hotels. They always live up to the Disney standard of excellence. I have personally stayed at two extremes: a Disney Value Resort (All Star Music) and a Deluxe Resort (Grand Floridian). I have never personally stayed in a Disney Moderate resort but, as the name dictates, those fall somewhere in the middle of Value and Deluxe. For families with young kids or couples wanting to save money, Value resorts can be a good option, especially in value season. The Grand Floridian is opulent, breathtaking, and you can't beat the convenience (right on the monorail track!). If you have a ton of money to spend (which most people don't), this is the way to go.
The bottom line: You need to decide what the hotel experience is worth to you. For my family (my dad, mom, and 3 siblings), the parks were everything. A hotel was just a place to crash at night, and we were all old enough to not need Disney transportation to take us back and forth from our hotel to the parks several times a day. On the other hand, some say if you're going to do Disney, go all out. If you foresee needing to go back to the hotel for a mid-afternoon nap or rest, you might want the Disney experience even when you're back at your hotel.
Once you've decided what you want out of your hotel experience, go from there. Research for the best rates, whether on Disney property or off. I've had wonderful experiences at both, although I must say there's nothing like a Disney resort to just complete the incredible experience :)
As always, email me or comment with any questions or to share your personal experience!