Besides Infocom's old z-machine, the text adventure language Inform can compile to a second virtual machine: Glulx. To play Glulx games, you'll need a Glulx interpreter such as Glulxe. (I am not making these names up, honest.) You can download a copy of Glulxe for Linux from the if-archive/programming/glulx/interpreters/glulxe directory of the IF Archive. Look for the Linux binaries. Download the tar.gz file and unpack it with the tar -xzf command. This will create two files, glulxeterm and glulxex. Once you get past all of the consonants in those names, you'll discover that the first file is the console version of Glulxe, and the latter is the X version. Use whichever you prefer.
As befits its reputation as an easy adventure language to learn, getting an AGT interpreter under Unix is a snap. The actual name of the interpreter is AGiliTy. You can get it from the if-archive/programming/agt/agility directory of the IF Archive. Look for the precompiled Linux version. Download the tgz file and unpack it with the tar -xzf command. This will produce a directory called something along the lines of agil-1.1.1. Inside that directory is the agil interpreter, along with several support files.
According to the readme which comes along with agil, the program expects filenames to be in lowercase, but most AGT games come in zip files with all-uppercase names. This isn't actually a problem, but if you'd like to make the names lowercase anyway, when you download an AGT game in a zip file, unzip it with the unzip -L command. The -L flag will convert all of the names to lowercase. Also, if you'd like you can use the agt2agx program to compact the many files of an AGT game into one .agx file to save space and make your life easier.
Alan is the only one of the interpreters for which source code is not available. You can get the interpreter from the if-archive/programming/alan/executables directory on the IF Archive. Look for the Alan interpreter for Glk with Linux executables. Download the .tar.gz file and unpack it. It'll create a new directory with a name like glkarun-2.86-linux-i386-2. Inside that directory will be the console version (glkarun), the X version (xarun), and the stdio version (cheaparun). Copy the one you want to save to a new directory and you can get rid of the rest of the files.