According to Disneyland, as of March 2008, there are 55 official "attractions" in Disneyland. However, many of those would not be considered "rides".
If we only consider what you could arguable call a "ride," then Disneyland has 36 rides:
Autopia, presented by Chevron
Davy Crockett's Explorer Canoes
Mad Tea Party
Roger Rabbit's Car Toon Spin
Big Thunder Mountain Railroad
Indiana Jones Adventure
Matterhorn Bobsleds
Space Mountain
Splash Mountain
Star Tours
Astro Orbitor
Buzz Lightyear Astro Blasters
Finding Nemo Submarine Voyage New
Gadget's Go Coaster, presented by Sparkle®
Haunted Mansion
Jungle Cruise
Mr. Toad's Wild Ride
Pirates of the Caribbean
Snow White's Scary Adventures
Alice in Wonderland
Casey Jr. Circus Train
Dumbo the Flying Elephant
"it's a small world"
King Arthur Carrousel
The Many Adventures of Winnie the Pooh
Peter Pan's Flight
Pinocchio's Daring Journey
Storybook Land Canal Boats
Disneyland® Monorail
Disneyland® Railroad
Fire Engine, presented by National Car Rental
Horse-Drawn Streetcars, presented by National Car Rental
Horseless Carriage, presented by National Car Rental
Mark Twain Riverboat
Omnibus, presented by National Car Rental
Sailing Ship Columbia