There's really not anything similar to the Blackberry Desktop Manager that you may be used to. However, there are many applications and settings that would provide you the same type of functionality found in BDM.
Back up your contacts? Use your Google account or export them to the SDcard.
Move pictures/videos/music to/from your phone and PC? Use the mass storage/disk drive mode to manage files.
Sync Calendar? Google would be your best option - but if you have another email account you can use the built-in Mail app or a hundred other sync apps from the Play Store.
Anything specific you were trying to do?