What separates independent clauses?

A comma and a coordinating conjunction (and, but, yet, or, for, nor, so). For example, the independent clauses, "We went to the ball game," and "It was a lot of fun," may be combined with a comma and the coordinating conjunction "but," as in, "We went to the ball game, and it was a lot of fun."

Also, "We went to the ball game, but it got rained out."

"We wanted to go to the ball game, yet we were getting tired of Baseball."

"We wanted to go to the ball game, or we wanted to go to the amusement park."

"We wanted to go to the ball game, for we had heard so many exciting things about the local baseball league."

"We would never go to a baseball game again, nor would we entertain the idea of it."

"We wanted to go to the baseball game, so we took off to get ideal seating."