I'm not a big fan of the mouse. I use it, I couldn't live without it, but if I can do something without using the mouse I will.
My first home computer was an IBM machine that didn't come with a visual operating system and you had to use line commands for absolutely everything.
When we upgraded to a Commodore Amiga it came with a mouse and visual navigation system based on the popular Apple designs of the time. My parents, completely computer illiterate, could now use a computer to do a few simple things like open a word processing document or keep a budget.
Even then, however, I found myself using keyboard shortcuts to get around. It's not that I didn't like using the mouse, I did, but it often seemed like it was the slower, less efficient way of doing things. Even now I have issues - you go to click on one thing and, snap, the dock pops up and suddenly I'm opening iPhoto. It takes a few minutes to open, tying up my computer the whole time, before I can close it again.
If you've ever used a mouse for a few hours in a row, like when you're playing a PC game, it can also hurt a little after a while. Frequent ailments include "mouse elbow" and carpal tunnel syndrome, which afflicts the hands.
The touch-sensitive mouse on laptops is also a pain in the behind. It's imprecise, the buttons are counter-intuitively placed and if you accidentally touch it with your wrist when you're typing something you might find yourself writing in the wrong place.
That's why I use shortcuts whenever possible.
Every operating system and program out there has shortcuts and you do yourself a favour by learning them.
Win+Home - Clears all but the active window.
Win+Space - All windows become transparent so you can see your desktop.
Win+Down Arrow - Minimize a window to the Taskbar.
Win+Up Arrow - Maximize a window to the top of the screen.
Win+Left or Right Arrow - This is the shortcut for the Window 7 "snap" feature, where you can drag an open window to one side to fill that half of the screen.
Win+Any Number - You can navigate to the items you've pinned to the Taskbar and then open by hitting Enter. If you add the Ctrl key you can navigate to a specific open window for that pinned application.
Win+T - Lets you focus and scroll through taskbar items.
Ctrl+Shift+N - Opens a new folder anywhere in Windows Explorer and certain programs.
Alt+Up - Moves up a rank in Windows Explorer.
This is only a sampling for navigating Windows 7, there are shortcuts for practically anything in any program and most programs will let you set your own - well worth doing to speed up time-intensive tasks.
Apple Snow Leopard
Control+F2 - Navigates to the top menu bar, then use arrow keys and Enter.
Control+F3 - Navigates to the Dock. (Does something different in Panther and previous OS)
Control+F5 - Move to the toolbar of the active window, then use arrow keys.
Command+Accent (top left by 1 key) - Move to the next window in an open application.
Cmd+Shift+Accent - Move to the previous window.
Cmd+Shift+N - Open new folder in a Finder Window.
Cmd+T - Quickly navigate between open programs.
The shortcuts are different for Windows and Mac computers, for obvious reasons. Some are universal, like tabbing your way through fields in an online form.
Jump to the Location Bar (so you can type in a new URL) - Apple is Cmd+L, PC is Ctrl+L
Move Back/Forward - Apple is Cmd+Left Arrow/Right, Windows is Alt+Left/Right
Find - Apple is Cmd+F, Windows is Ctrl+F
Open New Tab - Apple is Cmd+T, Windows is Ctrl+T
New Search - Apple is Cmd+K (to get to the Google search window), PC is Ctrl+K
Bookmark a Page - Apple is Cmd+D, PC is Ctrl+D
For word processing, spreadsheets, etc. you can easily find a list of time-saving shortcuts by doing a Google search - just type in the name of the programs and "shortcuts" and you'll get a list of more shortcuts than you know what to do with. I usually print out a list and highlight the ones I think I'll use the most. After a while I usually have those shortcuts memorized.