Where can I check how much Internet bandwidth did my HTC Desire use?
Mentioned 3G Watchdog probably is the best choice. Alternatively, you might want to take a look at...


NetCounter
Traffic Counter Extended
Mobile Counter
Net Traffic Counter


...which also cover your needs. Might be you like one of them more :)

Talking about more, I obviously missed...


Traffic Monitor
Traffic Monitor (same name -- other app; this one goes as deep as on per-app stats)