Try installing Audio Manager from the market to check your volume levels.
I had this problem when I first got my Tattoo and Audio Manager solved it. It allows you to see and control the alarm volume which is not that visible elsewhere. Audio Manager includes a widget that lets you see all the different volumes at a glance.
(You can actually change the alarm volume by
Clock > Alarm icon > select alarm > alarm sound > use hard volume controls to turn alarm volume up and down (it is independent of other sound settings)
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