My husband & I were married at Disney!
Alot of people buy those mickey bride and groom hats. We went to the Emporium and had Mickey and Minnie guest badges made that said "Just Married". We wanted them for souveniers but we wore them around the parks.
The monerail we were brought to the front, at cindy's table, they gave us champange glasses with cidrellas royal table scribed on them, in the candy store in MK the CM gaves us free fudge which I thought was so nice and in Epcot the CM at the beer stand gave DH a free beer on him. Alot of guest in lines congratulated us and one guy offered his condolences, (guess he and his wife were having a bad day) and at 50's prime time cafe, the waitress saw the badges and started yelling out "your cousins ran off and got married and didnt invite us!" and she brought out a cake and we had to stand in front of every one and feed each other. It was so cool! There is also a re-hiching ceremony in Epcot you could do.
We did get alot of attention, but I did have my two older kids (13,14 at that time) with me and they were getting a kick out of embarassing my poor new DH. So every chance they got they told CM's we were "Eww! on our honeymoon!"