I'd like to be able to have the Firefox "Connection Settings" and IE
"Lan Settings" buttons accessible on the browser's toolbar. Neither of
the browser's customizers provide this button. I'm constantly
switching between using a direct connection and a VPN (where I then
need to set a proxy), and I'm just looking to save a few mouse clicks.
Does anyone know if this is possible?

There is a fantastic extension for FireFox / Mozilla browsers called
SwitchProxy that will allow you to switch between proxy settings from
the toolbar.  (In addition, if you choose, you can set it to
periodically switch between anonymous proxies to provide more
anonymity in your web surfing.  Most interestingly, SwitchProxy works
well with Tor, the latest anonymity project from the Electronic
Frontier Foundation.  However, anonymous proxy switching is a
secondary feature that you do not need to use if you do not want to.)

SwitchProxy
https://addons.mozilla.org/extensions/moreinfo.php?application=firefox&id=125

Tor
http://tor.eff.org/




If you need something that works with Firefox, Internet Explorer, and
Opera, you may want to try another utility called Proxy Switcher. 
There is a free version of it called Switch Proxy Lite.  I have not
used it myself, but, it appears to have similar functionality.

Proxy Switcher and Proxy Switcher Lite
http://www.proxyswitcher.com/download.html




Proxy Changer also offers similar functionality, and may be worth
trying if you are not happy with the other options.  Apparently it is
targeted at Internet Explorer.

Proxy Changer
http://www.proxychanger.com/proxy-changer-download.asp




Finally, if for some reason you wanted to write your own script to do
this, you might find this article from Microsoft TechNet interesting.

Microsoft TechNet:  "Hey, Scripting Guy!"
http://www.microsoft.com/technet/scriptcenter/resources/qanda/may05/hey0519.mspx



I hope that helps.  If you have any questions about this answer,
please do not hesitate to post a clarification request prior to rating
the answer.  Thank you.


SwitchProxy
https://addons.mozilla.org/extensions/moreinfo.php?application=firefox&id=125

Tor
http://tor.eff.org/

Proxy Switcher and Proxy Switcher Lite
http://www.proxyswitcher.com/download.html

Proxy Changer
http://www.proxychanger.com/proxy-changer-download.asp

Microsoft TechNet:  "Hey, Scripting Guy!"
http://www.microsoft.com/technet/scriptcenter/resources/qanda/may05/hey0519.mspx




Search Strategy:  Search for SwitchProxy, then find similar tools for
other browsers

Search Keywords:  switch proxy Internet Explorer
://www.google.com/search?q=switch+proxy+Internet+Explorer

Excellent thorough answer. Certainly worth more then $2.00. Enjoy the $100.00 tip!

IBM provide tools for laptop computers, they can be used on standard pc.
I have one, that have profiles and can change proxy, lan settings,
homepage, ip configuration by one mouse click.

I have an IBM laptop and I'm using the "IBM Access Connections" tool.
However I haven't been able to change my proxy settings for the
Firefox browser. Do you know a way of doing this?