I have a new home and I was just wondering what size incandescent
light bulbs you can safely use in the screw in sockets in the garage
and basement? What about using one of those socket doublers to use two
light bulbs. Are those unsafe? Thanks!

I do understand your need for more light.  The limiting factors are the
material that makes the enclosure(plastic/glass), distance from the bulb
to the enclosure, material that the socket is made of (porcelain, bakelite,
plastic), apart from the maximum load on the particular branch(which may
be connected to other appliances simultaneously in the worst case).
You could also consider using the low watt high output flourescent lamps
(especially the one's with rare earth coating on the outer shell to produce
vibrant/bright white light).  If you want more output of the light being
produced by the tungsten lamps, you might think of a pressurized mercury
vapor lamp with a ballast(the downside is the high output of uv, apart from
the danger of explosion(since they run very hot)).

Regards
ldavinci-ga