Hi sugar_cube and Praxis - Welcome to the site
The only reasons that your unit should turn on (assuming it is not in its cradle connected to your PC - as AS wakes the unit up) are:
- a scheduled communications event (such as checking for mail, trying to sync via wifi, another programme trying to sync - such as eWallet, a weather programme, RSS programme etc etc)
- an appointment/ task reminder
- an alarm (set under clock)
- a scheduled back-up (or an automatic back-up being instigated due to battery level).
EDIT - thanks to minnesotagerbers -
- another reason my be HP Protection Tools can you temporarily disable them and see if that helps.
I can't think of another reason for it to happen.
Sugar_cube - if it is annoying you then perform a full back-up and then perform a hard reset and see if it still occurs (it shouldn't). If it recurrs after your first sync - then it is ActiveSync causing it. You could then load your programmes and see which one causes it

(of course you may decide to live with it

)