Number of visible supernovas exploding right now How many supernovas are going off (visible in principle) right now in the Universe?
 A: A typical number that people throw around is roughly a supernova per milky-way-like galaxy per century.  A more accurate, larger-scale, average number is something like a few times $10^{-4} \textrm{ Mpc}^{-3} \textrm{ yr}^{-1}$ ([1], [2]).  If we take the average sensitive distance to be a couple hundred Mpc, and assume that the average supernovae lasts a couple of weeks, that means that there are roughly 100 SNe visible in the entire sky at any given time (emphasis on the roughly).
How does this compare with survey observations?
Looking at the Palomar Transient Factory, they identify a few hundred supernovae per year, with a field of view of about 10% of the sky - which is consistent with about 100 at any given time.
It would be intersting to look at a more comprehensive list of supernovae and see how those numbers at up.
Now, if you're wondering about the entire universe: using the same numbers and something like $10^{12}$ galaxies, then something like a few supernovae go off every second.
A: As the comments question, it would depend if you meant the entire universe - which the answer could well be as Brandon Enright states - infinite.
But, in terms of what is visible to us, have a read of this rsponse by astronomer Phil Plait and the bottom of this NASA page, initially there was a single supernova visible every century or so, until the invention and refinement in observational techniques and equipment, now dozens are noted each year.
Hope this helps
