For this important point I would like to refer you to my longish comment on the last Higgs thread. The Higgs is only necessary to produce masses when those masses are forbidden by the symmetries of the standard model. Spin 0 particles like the Higgs are not constrained this way. That being said, it is true what Steve says, the higgs interacts with itself and thus gives us the mass it actually has.

Actually, Higgs' idea was to give the squared higgs mass an negative value to begin with, which destabilizes the vacuum and gives the higgs field itself a constant value in the vacuum, which in return through the higgs interaction with itself shifts the squared higgs mass to the stable positive value which we would observe now.

Comment 21 by davem :

This bear of little brain asks:

If the Higgs gives mass to other particles, how come it has mass itself?

Comment 22 by Steve Zara :

Comment 21 by davem

If the Higgs gives mass to other particles, how come it has mass itself?

Because it interacts with itself!