I am traveling and only have access to the internet (email and
financial data) while in Internet cafes/clubs.  Is there any way to
protect myself from having everything I do and type in logged, read
and stolen by the network administrators in these places?

The only real way to do it is to bring your own laptop and then use an
encrypted connection.  Typically most countries have wi-fi hotspots
that you should be able to connect to.

Assuming that this is not a possiblity, there is really no way to
guarentee that someone isn't logging your actions.  Here are some ways
to reduce risk....

1- Only use reputable internet cafes. 

2- Change your password frequently 

3- There is a program called "on screen keyboard" - you can launch it
(depending on permissions) by start-run-"osk"  This will prevent
keyloggers from getting your passwords (if you use the mouse to enter
the keystroke) but could still be picked up by more advanced
techniques (packet sniffers etc).

4-There are additional techniques - you could set up a VPN network
that requires RSA SecureIDs that require you to enter a code based on
a keychain fob that changes every 10 seconds or so- even if someone
gets your userid/password they will not be able to connect.  Then you
can store your passwords on your local machine and remote desktop in. 
Theoretically this should be un-crackable because you would need to
have a fresh time code, but it takes some work to set up....

http://anti-spyware-keypad.com/

I think there are two issues here. One is local spyware programs like
keyloggers, et cetera. These programs monitor what you type and where
you visit, and report that information to someone else.

To ensure you have no keylogging and similar software on your machine,
you should make sure you're running antivirus, antispyware and
antiadware software. You can find free and commercial recommendations
for each of these here:

http://www.andybrain.com/archive/free_spyware_and_virus_protection.htm

Now that your computer is "clean", you have to worry about your PC's
internet / network connection. A connection can easily be monitored by
anyone with some networking knowledge. To prevent this, make sure that
everything you transmit is encrypted. The earlier comment about a VPN
is the right way to go. This will encrypt data so that even if someone
sniffs your transmission, they won't be able to "read" it, and your
data is safe.

A VPN usually requires specialized software or hardware, and there are
many different ways of setting this up depending on your situation. It
usually does require you have your own equipment. Consult your network
administrator for help.