I use foreign keys quite often in my schemas because of data integrity, while my colleague has a no FK policy. His main argument is difficulties during data migrations which he frequently encounters. He rather have a smooth data migration process than having an unexpected error and abort the whole operation that the migration is only a small part of. I suspect the errors might be mainly caused by not considering data integrity at all at the first place, but I can feel his pain. To be fair, as far as I know, he never had major data problems.
He is not the only one I've met who insisted on not having FK. I've even seen large systems prohibit using JOIN statements.
Personally, I see the data integrity out weights the inconveniences, do you use FK for your systems, what are your experiences?
Another classic is the “joins are slow” argument, which I believe goes back to a period in the late 1990s when in one, not highly regarded at the time, database, namely MySQL, they were indeed slow. But the reason “everyone” knew about this was precisely the oddness of this situation: in fact RDBMSes are highly optimized pieces of software that are especially good at combining sets of data. Much better than ORMs, anyway, or, god forbid, whatever you cobble together on your own.
There is, in my mind, only one valid reason to not use foreign keys in a database schema. If your database is mostly write only, the additional overhead of generating the indexes for the foreign keys may slow you down a little (for reading, these very same foreign keys in fact speed things up quite considerably). Even in such a case, however, I’d argue you’re doing it wrong and there should be a cache of some sort before things are written out in bulk to a properly setup RDBMS.