I need to store a large table (several millions or rows) that contains a large number of user-defined fields (not known at compile time, but probably around 20 to 40 custom fiel
It seems like you've listed your available options. EAV can be a pain for querying (and slow, depending on how many criteria you want to search on simultaneously), but it tends to be the most "sane" and RDBMS-agnostic implementation.
Modifying the schema is a no-no...obviously it can be done, but such a practice is abhorrent. I do not approve.
The XML option is a solution, and SQL Server can query inside the structure. I'm not certain about other RDBMS's, and you don't list which one you're using in the post or the tags.
If you're going to be querying on many attributes (say, 20+) simultaneously, then I would probably recommend the XML solution just to limit the number of joins you'll have to make. Aside from that, I would stick with EAV.