The Brass Ring has quickly been growing on me to the point where it's probably one of my favorite bars in Madison now. I just started frequenting it about two months ago and it has a lot to offer. There is a bevy of pool tables so that it's almost a guarantee you'll be able to use one, the space inside is open allowing you to change-up what your doing on the fly without having to go somewhere else, and the beer selection is agreeable. There's also a shuffleboard table that is in good shape and usually not overcrowded (like the ridiculous "list" system the Great Dane uses). The atmosphere is good, but I think part of that is because I've usually gone with a group of 5 or 6 friends if not more.
There are a few cons though, despite the fact that I like it so much. First, the patrons there are a mixed bag. I don't like to judge other people, but it has a mix of trashy and cleaner looking people and I've heard of unsavory times there from friends of mine. I personally haven't run into any issues, but you never know. The bartenders are usually overworked and not very quick as others have mentioned, but if you snag a pool table it's usually not too big of a deal. Parking can sometimes be a hassle, but there's a lot of street parking if your patient.
Lastly, the food isn't that great. They give you big portions, but it's about as greasy-bar-food as it gets, and doesn't even taste that good. I guess I could recommend the chili-cheese-fries, but it's generally better just to get drinks, play pool, and get friends together. The Brass Ring's strong suit is it's open space, so invite a lot of friends and you're bound to have a pretty solid time.