Is there an application where I can see my banking account in real time or synchronized every hour or so?

Moved to Aftermarket Software

i dont know of any third party software that will do this automatically. But depending ony our bank, some do have a mobile version of their online banking sites. i know BoA has one and it works nicely.

Wirelessly posted (Verizon 8830: BlackBerry8830/4.2.2 Profile/MIDP-2.0 Configuration/CLDC-1.1 VendorID/105)

Bank of A$me
Bank of America has a site specific for mobile users. I am sure other banks as well.
See if MSN Money can be accessed to grab your bank feed.

Wachovia Bank does as well:

Wachovia Mobile