Object > Envelope Distort > Make with Warp > Bulge
set to a negative value will suffice in some occasions.
However, realize that using envelopes can sometimes result in undesired alterations. For example, they can occasionally distort verticals in way you don't want.
Many times for good text alterations it requires manual alteration of the forms. I'd say that particular TapOut logo was create by manually making the horizontals fit the desired shapes. You'll notice the first T has a very uneven curve to the top of it, jutting upward at the far left. The bottoms of the A and P do not line up and the bottom of the T on the right is much too curved to be correct.