First, there's Cracked. I know it was direct imitator of MAD with slightly less adult themes, but I didn't care. John Severin was an incredible artist (click here to see a page from his Hawaii 5-0 parody) and you had to love those monster themed issues!
Sometimes I wonder if the reason I know so much about every single TV show and movie that came out in the 1970's is because these magazines spoofed them all. There's no way I went to see Shampoo or One Flew Over the Cuckoo's Nest as a child, but there it was in MAD magazine.
Don't let the title of this post fool you - I still love to read these magazines, and MAD is the most enjoyable to me as an adult.
MAD had so many talented artists on its staff that each issue was a treasure to behold. All my issues of MAD have a deep crease on the back page due to Al Jaffee's fold page. I also loved Don Martin's stuff. Go here to see a sample of his off the wall works. I also enjoyed Spy v. Spy as well as the works of Sergio Aragones.
And there may be no better time capsule of the period than Dave Berg's "Lighter Side of..." series.
Then there was Crazy magazine published by Marvel Comics. The artists and writers weren't as talented as those at MAD, but it could still be irreverent and a lot of fun to read. I read it when their mascot was that little black sheik (Irving Nebish), but had gotten off the humor magazines by the time they switched to the infamous Obnoxio the Clown.
And finally, there was Dynamite magazine. Most kids got them through their Scholastic Book Club at school. Every cover was basically a stark background with a 70's icon on the cover. I still have a few of these - man are they a blast from the past! I seem to remember a magazine called Bananas that was very similar to Dynamite (help me out on this one - my memory is cloudy).