Just got an Ipad 2 for Xmas, so really new to this, but loving it so far. I manage a Mortgage Company and am a loan officer, so similar fields. So far here is what I've been doing with it:
Email - biggest thing, and like the stock Email app
Remote Desktop (using 2X Client app from iTunes FREE) - allows me to access my work PC (via Exchange Server) where ever I am
PDF Expert (from iTunes - $9.99) - allows you modify/sign PDFs - I'd think this would be a must have for realtors to have have clients sign contracts, etc.
Couple of mortgage calculators
DocsToGo ($16.99 in iTunes) - allows me to access Word, Excel, etc. files - the $16.99 version also allows you to sync files
Chimpadeedoo (free in iTunes) - easily add clients to my mailing list with Mail Chimp
I'm sure there is a lot more to uncover, but again I've had this bad boy for 4 days. Also, for signing contracts you may want to take a look at this stylus that is supposed to be released sometime in January (can't post links yet) Google Search "iPen Kickstarter" and it will be the first post.