I have been using the TDK XP SUPER Pro ST-160's. I have run about 4000 Hours on my adats with these tapes and never had a problem.
"From The Alesis Site"
What brand should I use?
Alesis currently packs a BASF tape with every new ADAT. BASF is a high-quality brand with strong professional support and we're glad to be associated with them. They also make a pre-formatted ADAT tape available which costs a little more, but saves time and keeps your heads cleaner.
Several other companies also make very good SVHS tape such as HHB, Maxell, Sony, TDK, and Quantegy. Some have made packages especially designed for the ADAT user. In any case, we strongly recommend that you buy your tape in a hardshell storage case if one is available. That will keep the tape cleaner and more stable when you put it on the shelf.