Every kind of files
<note> What means this title?
Good question, I think the only limit is just your immagination. </note>
Theory
The file server where all the homedir are stored has a high level of performance and security in order to prevent the lost or the manual deletion of files. From a theoretic point of view, it's better to use this file server to store every file we access and need, but after the theory start the practice and for now (I mean 202X decade) managing big files or huge amounts of small/medium files generate problems.
Practical
Currently you don't have limitation on the the type of files you want store in your homedir. The only limitations you are subject is the total disk space used by your files. At this moment all users share the same disk space (around 3.5 TeraByte) and we count on the personal attention to not overload the network and the file server. Although the disk space can appear huge, don't forget that all users of the network (the one you know, but also people you never meet physically) are using the same space, so pay attention. Maybe you didn't notice, but the dimension of files increase constantly. Maybe you don't know yet, but the high quality of the song or video you are watching in the left window just now means that the file is big. When I say big I mean BIG in terms of bytes used to store the whole. Networks simplified the transmission of data across the planet, but this don't means that the work is light, it's only hidden and performed by something else.
<note warning> For the moment the system is manageable, but don't try to find the boundaries of your possibility, the space used is checked by the System Administrators and if the homedir of one or more users are out of ordinary, they'll ask the users about this. </note>