Since no one has suggested my favorite method I'll chime in.
I figure that dropping various bits of hardware and other junk into
the hole is probably asking for some kind of trouble sooner or later,
so I replace the wood involved.

I use a plug cutter to make cross grain plugs; they're like a dowel
but with the wood grain running across the diameter rather than the
length of the rod.  When making them you can as easily make fifty as
one from a small piece of wood, so I keep a stock from maple, poplar,
mahogany, and oak so I can match the wood in question.  3/8" seems
about right for most holes.

When a screw strips, I drill out the hole with a brad point drill
with a depth stop matched to the size of my stock of plugs, pop
a little glue in the hole and pound in a plug.  (If you put the glue
on the plug it ends up all over the work surface, rather than in the
hole.)  Put just a whisper in the hole, though; you don't want a pool
of glue at the bottom of the hole that keeps the plug from going all
the way in.

If it's an exposed surface you can match the grain direction to make
a less-visible repair, leaving the plug a tad proud on insertion and
bringing it flush with a swipe or two of a block plane.  With a new
pilot hole you're driving your screw into solid wood, nearly as good
as new.  I find this takes about a minute longer than finding some
piece of junk to jam into the hole but is pretty fail-safe in terms
of a being a solid, permanent repair.

Using pre-made dowels from the store won't work because the grain runs
the wrong way: screwing into end grain provides little strength and
will strip again right away.

The glue I use depends on the situation.  If I'm in a hurry I use
Superglue.  If there's time (and there usually is -- 15 to 20 minutes
is plenty for the glue to grab) I use yellow carpenter's glue to set
the plug.  It's not something you will ever want to take apart.

This method doesn't work well for large screws in deep holes because
you can't usually pound in more than an inch or less of plug into
a size-matched hole.  For deeper holes the plugs need to be sanded
a bit undersize and then inserted with a strong gap-filling glue into
the deep hole (I use West 20 minute epoxy).  This becomes much more 
of a production than filling the smaller screw holes, but often these
are the screws most in need of their original strength.

Cheers,
Roger Wiegand
Wayland, Massachusetts, USA
www.band-organ.com