Some companies require that you have collision on your own car or buy their collision coverage, otherwise they reserve the right not to rent to you. Payless, L&M, and EZ come to mind. You need to bring proof of insurance, the page that describes all the kinds of coverage you have. During non-busy times they might not bother to ask for the proof of insurance.
If you have a credit card that provides both car rental collision coverage and car rental loss of use coverage, you need to decline the rental company's coverage. Things work out easier after an accident because the credit card company will put up a fuss about the loss of use and usually negotiates it down.
Disney hints:
http://members.aol.com/ajaynejr/disney.htm
<small>
9/65
Disneyland
3/75 World Inn (now Doubletree Club)
4/85 Kon-Tiki (now Econolodge Hawaiian)
'80s Disneyland once or twice
7/94 Dixie Landings (now Port Orleans Riverside)
9/97 All Star Music
11/98 ASMu & first premium annual pass
12/98 Knights Inn on 192
9/99 All Star Movies
12/00 All Star Sports & PAP#2
9/01 ASSp
11/01 ASSp
1/03 Motel 6 & ASSp & PAP#3
11/03 ASMu
8/04 Coronado Springs & PAP#4
8/04 again Motel 6 and Pop Century
1/05 PC
</small>