The BB BIS synchs every 15 minutes or so. The issue with Yahoo is that you need to premium from what I remember, $20/yr for the service.
Try this thread for more info on the Yahoo Issue:
http://www.blackberryforums.com/showthread.php?t=37942
Your AOL should be synch automatically, but again the BIS server only synchs every 15 minutes. Some email accounts like GMail, you can actually forward for instant synch...
Nothing to do with the phone, just the server whether you are on Cingular, Tmo, Verizon, or Sprint-Nextel...
ChattereMail is instant synch and pull when you set it to pull. I have/had a Treo 650 with ChattereMail and while I loathed the Treo, I loved Chatter...Similar to ProfiMail for Nokia S60 phones...