In South Park TV series, who is the father of Eric Cartman?
I have watched till season 10 and Eric's mother keeps on stalling the revealing of true identity of Eric's father.
It's his mother, Liane Cartman.
The episode is a 2 parter from Season 2 and near the end of the second part ("Cartman's Mom Is Still a Dirty Slut") in the hospital that Dr. Alphonse Mephesto was recovering in it's revealed that Liane is a Hermaphrodite and that the test indicated she was the father. A clue to this is how willingly Mr Garrison was to have sex with her given him being gay as indicated in how he showed up in the flash backs.
Following that Dr. Mephesto also mentions that since Liane is the father, she had to have gotten another woman pregnant at that dance who would be Eric's real mother. After another "Who is Eric's mother?" listing possible candidates (such as Sheila Broflovski which would really piss him off) Eric gives up on the idea.
Of course from the episodes I have seen it continues as if the episode never happened. I don't know if any other episode after that contradicted this personally however according to AJ's answer it is later contradicted in Season 14.
Since you are still at season 10, this will be a spoiler for you.
It is explained in season 14 episode 201 that Jack Tenorman (who was a player on the Denver Broncos) is his father. When Eric's mother was drunk, she and Jack had intercourse and Eric was born.
Scott Tenorman: Cuz you see, Eric, we have something in common. Did I ever tell you that my father played for the Denver Broncos?
Eric Cartman: No, no.
Scott Tenorman: The only Bronco who lived in South Park. He got a little bored one week And had an affair with a slut named Liane Cartman.
Eric Cartman: No, please!
Scott Tenorman: [to Dr. Mephesto] Tell him! You almost did before but you got shot by your brother who was a Bronco fan! Tell him!
Dr. Mephesto: It's true... Jack Tenorman was your father.