For backing up your system, there are a variety of methods at your disposal.
As you suggested, an external harddrive is one method. I think that usually, an external harddrive comes with a software package to backup your entire system like Symantecs "Ghost" software. That will do a complete backup of your system as it stands right now to the external hard drive.
Remember, that method will backup all the adware/spyware and viruses that are currently on your system as well as any of the 'quirks' that have accumulated since you first turned it on.
Remember, just backing up all the files on your computer doesn't backup everything in a usable fashion. You can't really backup your applications and then just copy them back after a system recovery and they work. When an installer installs an application (like Microsoft Office for example) it copies files into multiple directories and uses the windows registry to point to all of these files. So, you may not get them all..
If you have a limited amount of data to backup, here is my suggested list of files to be backed up (others feel free to add to the list).
For this, I'll be using Windows XP standard directory structure.
My Documents (this includes "My Pictures", "My Music", etc.)
Internet Explorer Favorites (C:documents and settings[user profile]Favorites)
Firefox Bookmarks (if you use it), do a search on "bookmarks.html" I believe.. Open the file to make sure it has your bookmarks in it)
Backup financial data (if you use quicken, MS Money, etc.)
E-mail (depends on what you use) (Outlook express is located C

ocuments and Settings[user profile]Local SettingsApplication DataIdentities{some weird identifying number}MicrosoftOutlook Express backup those files) (Outlook is a .pst file)
Address Book (C

ocuments and Settings[user profile]Application DataAddress Book
Anything Else (This is if you store things in crazy directories on the root of your computer or in some directory of a program in program files. I can't really tell you what that might be. It's what I look for when backing up a system)
-----------------------------------------------------
Accessing your system remotely.. again lots of options depending on what you want

If you don't need direct access to the system, you could carry a flash drive.
If you need direct access to the system, as suggested above, there is PC Anywhere, there's also GotoMyPC (I might even have an affiliate ID with them

) It's a monthly service fee for access anywhere with a web browser to your PC.. password protected on 2 levels (to login to GotoMyPC and then to actually connect to the PC once logged into their site).
Sorry to ramble, hope it helps. Have a Happy Thanksgiving!!