This article is from the X-Men Comic Books FAQ, by Kate the Short (firstname.lastname@example.org) with numerous contributions by others.
Capitalism. The rich get richer.
Apparently, the Xaviers are an old money family, since the Graymalkin
estate (and the many-times rebuilt mansion) has been described as being
in the Xavier family for ten generations. So, Charles Xavier inherited
a lot of money. Xavier also has decent ties to the Avengers and to Reed
Richards of the Fantastic Four to get cheap access to funky technology
(as the easiest two examples: the image inducer was invented by Tony
Stark, and the unstable molecule costumes were made of fabric obviously
supplied by Richards). Finally, Professor X was formerly the consort of
an intergalactic queen (Lilandra), and got a bunch of cheap, high-tech
alien goods and repairs passed under the bed, as it were.
Among the cheap, high tech alien goods was a handy-dandy costume
machine, which presumably works with Reed Richards' unstable molecule
fabric. Hence the X-Men aren't spending a lot of money on clothing.
Which is a good thing, considering how costumes they go through on your
When Xavier's own money has been inaccessible, Warren Worthington has
been there to step in. He had a lot of money to start with, and appears
to have regained the money Hodge took from him when Warren "died". Note
that Emma Frost and Betsy Braddock are also financially well off.