What other applications? It is an isotope used in some night sights for firearms, and for a while it was a hydrogen bomb component candidate, but the relatively short half life (abt 12 years) makes it kind of useless for that too. Tritium is about as useful as the garbage in a landfill.
It is used in medical research for a number of applications. For example, one can measure the kinetics of enzyme/substrate binding using tritiated substrates.
It is nice to work with because it has such low energy that the researcher has no worries of the beta particles penetrating the skin.