There are several 'super-interpreters' which support basically all common game formats. Unless you know what you are doing, this might be your best bet: Gargoyle, Spatterlight, Zoom.
Typical file extensions of Z-Code games are .z1, .z2, .z3, .z4, .z5, .z6, .z7 and .z8 (very rarely, you'll find .dat). To run these games, Frotz is usually a good choice.
Glulx is meant as a successor of Z-Code. The games can be recognized by the extension .ulx or .gblorb. The reference interpreter is Glulxe.
TADS2 games usually end in .gam, TADS3 in .t3. TADS interpreters exist for most platforms as well.
Alan games always come with two files. Version 2 usually uses the file extensions .acd and .dat, version 3 uses the combination of .a3c and .a3r. Interpreters for both Alan versions can be found through the official site.