NatWest Internet Banking
To begin with, unlike competitors, the demo for NatWest internet banking is exactly that- a complete walkthrough rather than a slide show; so you'll know exactly what you're going to get.
For information across any of your accounts, you can view balances, mini-statements or complete statements; or indeed download whole statements to your PC. For transfers, you can move money instantly between your accounts, or move money to any other UK-based bank account. Bill payments and standing orders can be set up or amended (including a scheduler so you can pay bills while you're off on holiday). You can of course also apply for various services.
The NatWest internet banking package downloads are excellent- the service is compatible with MS Money, Quicken, Sage and Excel, and a great feature is automatically downloading data since your last visit (the "last visit" concept is also used as a security measure).
The NatWest internet banking service has been through several iterations since they first launched, and they're pretty much on the button now. The only complaint is that a little extra product, the financial planner, just isn't as clever as it could be; but even so that's an extra that other banks don't offer, so no real complaints.