How much continuous power can a 30 A 240 V outlet handle?
Use the 80% rule for continuous loads (because the breaker will, even if you don't)

While 210.22 would seem to indicate that you have the full 30A available to you:


  210.22 Permissible Loads, Individual Branch Circuits.
  An individual branch circuit shall be permitted to supply
  any load for which it is rated, but in no case shall the load
  exceed the branch-circuit ampere rating.


you have to consider that the breaker may have other ideas, as stated in 210.20(A):


  (A) Continuous and Noncontinuous Loads. Where a
  branch circuit supplies continuous loads or any combination of continuous and noncontinuous loads, the rating of
  the overcurrent device shall not be less than the noncontinuous load plus 125 percent of the continuous load.
  
  Exception: Where the assembly, including the overcurrent
  devices protecting the branch circuit(s), is listed for operation at 100 percent of its rating, the ampere rating of the
  overcurrent device shall be permitted to be not less than 
  the sum of the continuous load plus the noncontinuous load.


The reason why is because garden-variety breakers made to UL 489 (and their counterparts in fuse-land) will eventually trip (or blow) if you run 100% of their rated current through them for hours on end.  While there is such a thing as a 100%-rated breaker, they are typically only found in industrial work.

Furthermore, the branch circuit wiring needs an 80% derate for continuous loads as well, as per 210.19(A)(1):


  (1) General. Branch-circuit conductors shall have an ampacity not less than the maximum load to be served. Conductors shall be sized to carry not less than the larger of
  210.19(A)(1)(a) or (b).
  
  (a) Where a branch circuit supplies continuous loads
  or any combination of continuous and noncontinuous loads,
  the minimum branch-circuit conductor size shall have an
  allowable ampacity not less than the noncontinuous load
  plus 125 percent of the continuous load.
  
  (b) The minimum branch-circuit conductor size shall
  have an allowable ampacity not less than the maximum
  load to be served after the application of any adjustment or
  correction factors.
  
  Exception: If the assembly, including the overcurrent devices protecting the branch circuit(s), is listed for operation
  at 100 percent of its rating, the allowable ampacity of the
  branch-circuit conductors shall be permitted to be not less
  than the sum of the continuous load plus the noncontinuous
  load.


So, you're limited to 5760W for an on-all-the-time (or at least longer than a few hours at a time) load.  Non-continuous loads (say a large well pump motor), though, can pull the full 7200W from the circuit as the duty cycle of the load provides adequate time for things to cool off between runs.