Home Depot sells a heavy-duty mirror/picture hanger that doesn't need a
stud. It's in the picture-hanger section, OOK brand. It's supposed to be
able to hold 100 pounds or something like that. It uses several, angled
nails into the sheetrock.

We have a reasonably heavy vanity mirror that I've used one of these to hang
for about 5 years now. I was dubious, but since the mirror is probably
closer to 40 pounds and the thing was rated for 100, I decided to try it--
so far so good.

In our old house, I put nails into the studs, which didn't end up where I
wanted the mirror, so I had to put them at different heights so it would
work out and center where I wanted it to. The OOK hanger was sure easier.

As for the person who said "don't use wire" on a heavy mirror -- it can
work, you just need heavy-duty wire. Our mirror is hung with wire, and it's
a thick, twisted piece much, much heavier than standard picture wire
(actually it might be the same stuff, just lots of pieces twisted together).

-Tim