Corporate rivals Marvel and DC first teamed up in the 70s; an adaptation of The Wizard of Oz was followed by two Superman/Spider-man team-ups. These set the tone for many pairings that followed, by positing that the characters always shared the same universe. Despite their apparent shared reality, Superman remains the overpowered Silver Age hero, while Peter "Spiderman" Parker lives his classic, complicated double life.
Later crossovers had the characters living in parallel universes, despite the fact that DC and Marvel's house styles have grown increasingly similar since the 1970s.
I've written a more complete account of Superman vs. the Amazing Spider-man which appears off-site at E2.
The second Superman/Spider-man team-up featured Wonder Woman and the Incredible Hulk, seen here on the back cover. Further information on this comic appears here.