Not sure why people are saying it would be useless.. Contrary to the above, I think it's not very impactful for contact management -- anyone can come up with a workable solution for maintaining contacts.
Databases are useful in almost any business which, unsurprisingly, deals with data. Trading is highly data intensive, also unsurprisingly. A couple examples where you might use a database in trading are:
-- Maintaining information such as parameters for a large set of products.
-- Storing your trades and other useful information associated with said trades. This would be especially useful when you want to look back at the trades and filter/process them in various ways to try to learn about what you're doing well/poorly. Using a database allows you to query stuff on the fly when you think of different ways to examine your own data.
-- Various operational stuff like maintaining positions, account information, etc. You want to be able to query these in an interactive way if you want to be able to aggregate your positions in different ways on the fly, which can be useful for evaluating the risk of your portfolio.
Let's try to make uninformed claims less often..