Generally, unless your incomes are identical, someone will have to pay some amount of support to someone else. Even when the incomes are identical, a support award may be made for a variety reasons. Judges don't seem to like custody cases where support isn't awarded, whether it makes sense or not. In many joint custody arrangements, the amount of child support paid is less, since the children's time is more equally divided between the two parent's households.
The reduced support is often cited frequently by the prospective custodial parent (most often the mother) as the main reason the other parent (usually the father) is seeking joint custody.
(See Defusing Objections To Joint Custody for a more detailed write-up on this particular argument against joint custody.)
How long should I keep the receipts showing the child support I've paid?
Forever. When we say "forever", we mean "until you die", and we're not kidding. Read this portion of a message from one of the SPARC Message boards for a nice example of why we make that recommendation:
"...someone we don't see round these parts much anymore was exactly in the same position. Apparently the bio-mother worked in finance and realized that banks purge their records after 10 years, including microfiche. She also realized that her ex-husband didn't keep great records and knew that he depended on the bank to do so. She went back to court saying that he was behind $23,000 in child support from 10 years ago (how convenient!) and since he didn't have any proof (bank couldn't provide it) he was out of luck."
Now if THAT doesn't convince you to want to "be buried" with your records, we don't know what will.