How many tubes?

none? one if you like to be prepared. 

The norm is probably one.  But you can carry two if you are extra cautious.  Or feeling particularly unlucky. 

I always carry a small saddle bag with 2 tubes and 2 CO2's.

At least one, sometimes two if my setup allows for it. For my first HIM I had one in the bag and another rolled up and tucked in between the bars on the bottom of my seat. Worked great and luckily I didn't need them. 

I now carry two for any ride.  I bought a Torhan's VR bottle and converted it to storage for tubes, CO2, levers, patch kit, etc.

My rule:

0 for sprint and oly

1 for HIM

2 for IM

x2

Two for a HIM since neutral support can be sketchy.  You might wait over 30 minutes to get help, so you may as well fix your flat and get on with it.  The race only gets harder as the day goes on and temperatures rise, especially where I race, so taking a 30 minute "break" isn't going to make you feel any better.

I don't actually think it's likely you will get two flats that are independent of each other...but usually in a race the first flat I will change as quickly as possible with very little care if there is something still stuck in my tire.  Keeping my time losses under 3 minutes is at a premium because goals are still in play.  Taking the time to do a full tire inspection would likely put me outside that 3 minute window.  But if I got a second flat because there was something still stuck in my tire...goals are out.  I'll take the 7-10 minutes to change my tube properly, but at the same time will not be at the mercy of neutral support and can still finish my race within 10-15 minutes of my goal time (assuming all else equal).

Then of course there is the possibility of hitting a big pot hole and getting a double flat...where one tube doesn't really help you.  Usually for a HIM, you're carrying two bottles and nutrition anyway, so hiding two tubes usually isn't that big a deal.  I'd say there is around 0-15 seconds time penalty for me carrying it.