Z-code games are, to some extent, the most complex of the ones discussed in this article. Z-code games are written for a virtual machine known as the z-machine, which was developed by Infocom. All of Infocom's text adventures ran on the z-machine, and the text adventure language Inform creates z-code games by default.
Z-code game files come in several varieties: .z3, .z5, .z8, and sometimes .dat. The different filename extensions have to do with what specific flavor of the z-machine they are supposed to run on, but since z-code interpreters will run any of these without complaint, you don't have to worry about these details.
Most z-machine interpreters are variants on one of two basic types, Frotz and Zip. (No, not Zip as in "zipping files up to compress them". I know. It confuses me, too.) On some platforms Zip is preferred; on others, Frotz. Your best bet is to get your interpreter from a page such as this one. There are umpty-ump billion z-code games, which you can get from the /if-archive/games/zcode directory of the IF Archive.
Once upon a time AGT bestrode the world of amateur interactive fiction like a Sauroposeidon. And like that dinosaur, AGT is not seen as often as it once was. There are still a lot of games available written using this program. AGT games can generally be recognized by the sheer number of files they come in: .d$$, .da1, .da2, and so on through .da6, along with .ttl, .ins, .voc, .opt, and sometimes .cfg. (Did I mention that AGT games come in many many files? I was not lying.) Because of this, AGT games are almost always bundled as zip files. Very rarely you will see a game come in just one .agx file -- more on that in a moment.
The AGT interpreter was originally only available for MS-DOS, but Robert Masenten wrote AGiliTy. AGiliTy is available for many computers. In addition, AGiliTy has the ability to take all of the files mentioned above and replace them with one .agx file. You can get AGT games from the /if-archive/games/agt directory of the IF Archive.