In the mountain bike world, you can run most any tire you want as long as you use either a tubeless ready rim or one of Stan's rim conversion kits (primarily a special rubber rim strip that has a valve stem on it). The conversion kits are what most folks were using several years ago (these kits consist of the thin plastic rim tape, special rubber rim strip with valve stem attached, and sealant) but nowadays there are a lot more tubeless-ready rims on the market. What you're doing with the kit is "converting" a standard mtb rim to a tubeless rim. The tire choice is not as critical because they're run at much lower psi; on my 29er I run 30 psi rear and about 25 psi front. I always advise folks that if they plan to run their mtb tires higher than 40 psi then tubeless is not for them. The main benefit is that lower pressures give better traction and ride quality off road without worry of a pinch flat. If you plan to run anything higher than 40 psi, it negates that anyway. I will say this: there are a LOT more "tubeless ready" tires on the market nowadays than there were just two or three years ago. If you plan to run tubeless on a mountain bike, you might as well use a tubeless-ready tire. The difference is the tire's bead is probably a little stouter, and the sidewalls are probably a little stiffer.

With cyclocross tires, kind of in-between road and mountain, folks are experimenting, just kind of doing whatever works in regard to tubeless. Our shop sponsors a small team, and honestly, there's no way I could explain all the different things they do with their tires. I really don't even know. Seems like everybody has their own ideas and thoughts on the matter.