I myself use the mouse almost exclusively. To paraphrase Sherlock Holmes, why clutter up my mind with a bunch of extraneous info when I can do it with the mouse easily and painlessly?
But I know a lot of you I am sure use the hotkeys instead. Just curious as to what all your preferences are.
I use a drawing tablet instead of a mouse. 
I use both. I find I can maximize my navigational speed by knowing shortcuts and keystrokes to rapidly do what would take many mouse clicks to do the same thing.
Windows-E, Windows-Break, Alt-Print, Ctrl-X, Ctrl-C, Ctrl-V, Ctrl-Z, Ctrl-B, Ctrl-I are the ones I make the most use out of. There are many more that I use.
Jim
I use the mouse for everything except enlarging text size. Ctrl and the arrow keys are marvelous!
Bit of both. I use the mouse most of the time, but I use the shortcuts for cut, copy, paste and new Firefox tabs. I’m sure if I wanted to I could get used to using more shortcuts, I just haven’t bothered learning them.
:smack: It’s not Ctrl and arrow keys, it’s Ctrl and the scroll thingie on the mouse that enlarges text.
(Just in case someone was wondering why nothing happened when they did Ctrl-Arrow.)
I use a little bit of both.
Always the mouse. I’m so enamored of the mouse, in fact, that I also use one with the laptop whenever I can.
I use the keyboard as much as possible. It always irritates me to have to move my hand fromt eh keyboard to the mouse and back. I even play Freecell usng just the keyboard controls, which tkaes a bit of getting used to.
StG
I like the mouse for most things other than Ctl-A, Ctl-C, and Ctl-V…oh and Ctl-N. Other than that, my brain is full. 
I use both. Depends on the situation.
⌘-o, ⌘-p, ⌘-i, ⌘-w, ⌘-n, ⌘-f, ⌘-
And apparently one such key combo tells vBulletin to go ahead and post!
If it’s a new program I’ve never used before, I’ll use the mouse until I learn what keystrokes do what.
I use the hotkeys because I’m a touch typist and it’s a major slowdown to have to stop what I’m doing and reach for the mouse. Obviously different if I’m in a drawing program and mostly using the mouse already anyhow.
Like Ruby - mainly the mouse, aside from the classics.
Mostly the mouse. I use some lefthanded hotkeys, so I don’t have to take my right hand from the mouse, but since I have to look to use numbers, capital numbers, and F-keys, I’m limited.
I use the hotkeys as much as possible.
In work, I use Excel quite a bit and it helps to know Ctrl + Shift + 1 creates the “2 decimal and commas” format, ALT and “+ key” yields the sum function, and so on.
I use the computer a lot at work and at home. Among other things I have heard that using the mouse excessively might cause carpal tunnel syndrome due to the enormous amount of repetitive right index finger motions.
I use a lot of hotkeys, not just the universal ones already mentioned, but also the application-specific ones like in Adobe Photoshop and Premiere, or in Lightwave.
It bothers me when the standard ones do not apply, though (like when Ctrl-F is not the “Find” key in Outlook, and instead means “Forward”. Stupid Microsoft.)
Though I’m not a computer, I think I’m still qualified to answer your question. I like to know the hotkeys, and I use them a lot; my Linux days still inform my sensibilities. However, I use the extra buttons on my fancy Kensington mouse to go back and forward in my browser, etc., and I try to rely as little on the keyboard as possible when gaming. Back in the Quake I days I actually mapped right click to “run forward”. Can’t do that anymore, since weapons have secondary fire now, but if I could map the extra buttons on my mice to in-game functions, I would.
Both. Mouse and Hotkeys, depending on how I feel and how fucked up my wrist is at that point in time. If my RSI gets too painful in my mousing hand and I don’t feel like going through the palaver to switch the mouse to the other side of my desk, then I’ll start using the hotkeys.
I mostly use hotkeys once I have them committed to memory. I find using them to be much faster than clicking with the mouse.