The way to say 'I need a haircut' in Spanish is the following:

-Necesito un corte de pelo
(I need a haircut)

I will add some more vocabulary that might be useful if you go to the hairdresser's:
-Laveme el pelo por favor
(wash my hair please)
-Necesito un afeitado por favor
(I need a shave please)
-Dejemelo el flequillo largo
(leave my fringe long)
-Mas corto
(shorter)
Asi esta perfecto!
(Perfect!)