Are tubular tires still used today?
I alternated tubulars and clinchers (different wheelsets) on my commuter bike for over a year and it was clear that I had fewer punctures with tubulars.  In fact, I have so few punctures that I have to reglue tires after a year or so since the glue dries up.  YMMV.


when a tubular does flat, you almost never get a catastrophic deflation (bang), you get slow leaks. 
if you're careful you can ride on a flat.  I finished the last mile (uphill) of a race on a flat.
they are more comfortable, especially when cornering because of the suppleness of the side walls.
you can get a sub 1500 gram wheelset for well under $500 (Campy Record and Mavic Reflex).  Try that with clinchers.  Tubular wheelsets are generally much lighter than clinchers.
if you do get a slow leak, tufo or stan's tire sealant will almost certainly fix it.


Now all of my bikes run tubulars.  For my commuter bike I use Tufos which last forever despite the broken glass that you inevitably see on roads. For racing Veloflex are superb.  And as was mentioned tubulars dominate the cyclocross scene.

Once you get the hang of gluing, it's not really a big deal.  The main disadvantage in cyclocross is that you need multiple wheelsets to be able to shift tires on short notice due to weather changes.  Dry vs mud, say, requires two completely different treads.

Finally, for most places in the US you have little choice but to buy your tubulars off the web since the LBS is unlikely to stock them.  See: http://www.worldclasscycles.com/tubulars.htm