If you want Push Mail on BlackBerry without BIS/BES (or with other phone)
Try Shang Mail Service: http://en.shangmail.com/
To use Shangmail service on BlackBerry phone you must have BlackBerry Email Service Book.
Follow the guide how to Enable BlackBerry Browser to know how to add Service Book to BlackBerry
If you dont need Browser, you can add Email Service Book very quick follow here:
1. Connect BlackBerry to PC use BDM
2. Open Backup and Restore
3. Go to Advanced
Open Service Book backup which have Email Service Book (check Service Book page)
Import to BlackBerry device.
4. Test compose a Email.
Note: if you do the Import you will lost current Service Book on your BlackBerry.