Alamo and National have a number of offices on site. Car Care Center, Dolphin Hotel, and the Buena Vista Palace. If you rent from the CCC, they will send a shuttle to your resort. They will not pick up or drop off at theme parks. You can also take a Downtown Disney bus and walk across the street to the BVP. If you are at an Epcot resort, the Dolphin is the easiest location to get to. Either that, or pick it up after a day at Epcot or the Studios and take the boat back to the Dolphin.
Avis is located at the Hilton. Again, take a DD bus and walk across the street.
Dollar is at the Regal Sun Resort (formerly the Grosvenor). It is also located across the street from DD.
Budget is at the Doubletree Guest Suites, which is a further walk from DD bus stops, but evidently they will pick you up if you arrange in advance.
Enterprise is located at the Hyatt Regency Grand Cypress and they will pick you up.
Hertz is at the Marriott Village (on the other side of I-4) and they will pick you up.
We have rented at FLL airport and they charge high fees if you pick up from the airport. Definitely compare prices with picking up at WDW. We have never been charged a drop fee and we have rented at MCO and dropped off at WDW, or rented at WDW and dropped off at FLL, etc. There usually isn't a drop fee in Florida, but read the fine print!
We have found the best rates through Costco.