They do have music exams in the US. I used to take them in piano when I was in primary/ secondary school.
However, my daughter has just taken the Grade 3 piano exam here in the UK and they are much more demanding in terms of technique and theory than the US. They involve playing three pieces (from a book with various selections), a selection of scales, an aural test, a sightreading test and possibly some other questions about pitch/ rhythm from a piece.
I have accompanied for theatre, choirs and soloists and I also wondered at what level I would be graded. Basically, after grade 8 you can obtain a diploma and are playing at professional level standard. Through ABRSM, you can obtain diplomas and licentiates to teach as well.
The best way to find out what level you are at is to flip through the ABRSM books at your local music shop, and judge at what level you are comfortable playing. Their website is very helpful as well. The exams are quite expensive (44 pounds for grade 3), but if it helps you to be able to allow others to identify the level at which you play, I think it is worth it.
I believe the exams help to motivate my daughter to practice and develop. Also, the work she is doing is rewarded with a recognized diploma for the standard she can play.