iSSH (App Store link) is a Secured SHell client for iPhone that works over any data network, cellular or WiFi. It is easily one of my favorite apps for a number of reasons. The biggest reason is obvious: I can remotely manage my server(s) from literally anywhere. Other reasons include a very intuitive user interface and the ability to use pretty much any meta key you would ever need.
Here is me watching someone’s NetHack game in iSSH:

The first thing you will notice about iSSH is that the keyboard is transparent so that you can see more lines of terminal and still be able to type.
Here is a similar screen of a server running htop:

Another great feature of iSSH is multitasking. iSSH can stay logged in for up to ten minutes after you leave the application (10 minutes is Apple’s limit). This is great for quickly switching between other applications that you’re using. iSSH will send you a message alerting you that your connections will be closed if you don’t reopen the application within a few minutes of the ten minute limit.
SSH isn’t the only thing that iSSH can do. It can handle VNC connections for viewing servers and desktops (of any OS) remotely. The new version of iSSH can even set up tunnels through SSH so that you can take ports from the connected host and forward them to your iPhone locally.
For instance, I have forwarded port 80 from my server to my iPhone on port 8080. Note that it looks like I’m running that server locally:

iSSH is undoubtedly one of the most feature-filled SSH/VNC/Telnet client for iPhone. It is definitely one of my favorite apps. I highly recommend it. It is updated on what seems to be a bi-weekly basis with new features and bug fixes. iSSH is easily the most frequently updated iPhone app that I own.
The only drawback is the price: $9.99 USD. If you ask me, iSSH is worth $50.
The full feature list:
• Multitasking support – can hold connections open for up to 10 minutes
• Arbitrary port tunneling through SSH
• Tunneled VNC client (or unencrypted using a “raw” connection)
• Tunneled X server
• Support for any non-standard ssh or vnc port
• Multiple simultaneous connections
• iPhone 3.0 cut and paste (double tap in console)
• Nearly every encoding supported
• Reachability notification
• Features a VGA BBS ANSI compatible font
• Portrait and landscape mode
• 53×24 or 80×24 (user configurable on iPad) with scroll-back buffer
• Arrow keys (by pop-up or by toolbar). Ctrl, alt, esc, tab, shift, Fn keys (1-10), ` key, all in combination.
• Keys are highlighted to confirm combination.
• Store any number of connections and configurations
• Command execution on connection
• Transparent keyboard
• Four (six on iPad) selectable monospaced fonts
• Via EDGE, WiFi or 3G
• RSA and DSA key generation and exchange via email, password-connected SSH or pasteboard
• Can support “uninterrupted” connections via GNU Screen and the command option.
• Transfers public keys automatically, without needing to email first.
• Pinch zooming in VNC/X11
• As good or better bluetooth/dock keyboard support than other VNC/RDP and console apps in the App Store! (Please follow iTunes support link for details.)