First, you need to allow the compter you want to remotely control to be controlled. Launch Remote Control Preferences, and allow Ubuntu to be remotely controlled. You can also set a password if you want. You can now control that computer remotely from another Ubuntu computer. Make sure to choose the VNC protocol when connecting to the computer. If you would like to control Windows 7 from Ubuntu, you need to choose the RDP protocol (You will need to have remote control allowed on the Windows 7 computer).

I know that this is not the place where to make Android Recommendations but the original question is about an Android APP.

If you wish to SSH your Computer, which is indeed different than "Remote control" which can be achieved by a VNC/Teamviewer Application in a tablet, you may wish to give a chance to JuiceSSH.

JuiceSSH Free Version includes the next features:

The all in one terminal client for Android including SSH, Local Shell, Mosh and Telnet support.

Features:

• Full colour terminal / ssh client
• Popup keyboard with all those normally hard to find characters
• Use the volume keys to quickly change font size
• External keyboard support
• Official Mosh support (http://mosh.mit.edu)
• Telnet support
• Local Android terminal support
• Click URLs to open in a browser
• Copy & Paste within sessions
• Save / Share SSH transcripts to Dropbox/Evernote/Email & SD card
• UTF-8 character support
• Easily organise your connections by group
• Keep multiple SSH sessions running in the background
• Seamlessly connect 'via' other SSH connections with one click
• Immediate access when you open the app to your frequently used connections
• Password & OpenSSH private key support
• SSH key agent forwarding
• Support for two-factor authentication (eg: Google Authenticator)
• Identities (users/password/keys) are abstracted from connections. Instead of updating every connection when you change your password - just update the identity and any connections linked to it will use the new password/key.
• Works out of the box with Ubuntu, RedHat, CentOS, Mint, Gentoo and all other flavours of Linux
• zlib compression to improve SSH sessions on high latency connections

I use it for the day-to-day administration of a self hosted server and it is really useful, you feel like being inside of an Ubuntu Terminal.

Some screenshot from my sessions (documented in my blog) are placed here to illustrate some tasks.

JuiceSSH and irssi for connections to IRC servers/channels.

JuiceSSH installing emacs in the server, which can also be used via JuiceSSH

ASCII based representation of an image in the server, really useful in order to see what is the picture.

The usage of JuiceSSH is really simple. You create the profiles which will include the username and password, then create the servers and use both in conjunction in order to make a connection, which means that if you admin more than one server, the same profile may be applied to many of them.

Remember to make the server reachable via LAN/WAN by allowing the Firewall the connections via port 22 in your favorite Firewall application. I use Firestarter in Ubuntu 12.04 and it does an awesome work so far. For external connections remember to forward the port 22 to the proper IP/Device where appropriate.

If you need further support or this answer doesn't fit your needs don't hesitate to drop a comment.

Good luck!

P.S. When SSH'ing a server, Midnight Commander and its included mcEdit text editor will be your best friends. Just a suggestion. :D