I used to use it a whole bunch, but my use has tapered off after I 1) installed the Scrollbar Anywhere for Firefox and 2) bought a mouse with a shitty wheel.
Well I just used the wheel to get here so I’m another that would buy a new mouse.
Yes I am a big scroller especially in Firefox. In addition to its regular use, I use the scroll-wheel button to open a link in a new tab. And I use the “scroll anywhere” addon which lets me lock into scroll mode by clicking and briefly holding the scroll button. Extremely convenient for navigating large pages and I miss this feature immediately when I have to use IE.
Yes. Not only do I use it I have 2 spare mice in case I need to breed them.
My monitor has a depressingly low refresh rate, so I tend to use the Page Up/Down buttons for my scrolling purposes.
I would like to have the more precise scrolling of the wheel, but alas, t’was not to be. 
I’d definitely buy a new one. Though I’d hate to since it’d run me about $100 bucks for another mouse this good.
Yes. I’d hate to try and browse the Dope without a scrollwheel. So many people’s posts to skip…
No scroll wheel? New mouse.
Tennis elbow cured my scrollaholicism.
I could make do for a while, I think. I use it quite a lot, but I use the keyboard PageUp/PageDn/Home/End keys just as often. I definitely would replace it eventually, once the annoyance factor reaches the laziness threshold.
As I discovered from repairing my cheapass, ancient (1997 IIRC) Logitech mouse, the “click” comes from a bit of plastic around the wheel axle, that acts as a kind of flexible latch thingy. It fell off as I was scrubbing the wheel itself and I couldn’t find it again, let alone re-install it.
Now my scrollwheel is just clicklessly freewheeling, works perfectly fine, and is much more comfortable and precise that way. Hurray for DIY and messing about with screwdrivers 
It’d drive me berserk to not have the wheel. Mine started slipping, so I cut grooves into it to make it easier to grip. Then it lost nearly all its cohesion, so I opened the mouse and superglued the external wheel to the internal one. Haven’t had a problem since.
My computer at work has a center lever, which is vaguely annoying because you can’t scroll all that fast with it. I find it tolerable for most purposes, however.
I use it all the time even in my Kensington Pro Mouse whose ring is around the cueball, which is clunky, but still less clunky than hoping your aim is good in scrolling down and up documents with either Pro- or regular mice.
In fact, every time I see this thread title in the forum listing it has been displayed after using the scroll wheel to reveal it.
Last time I was at my Dad’s I was using his computer and he said “what’s that you’re doing?” I’m like “What?” took awhile before I realized what he was talking about as I was navigating thru a web page because I do it without realizing it now.
I use mine so much, I’ve been through several mice trying to find the best one. I finally settled on the Logitech MX wireless. Not perfect, but the best so far.
Oh, and the two-fingered scroll on the MacBook? Best. Invention. Evar.
I use the wheel for almost all scrolling. We have a few applications that don’t support it but I always try anyway before reverting to clicking on the scrollbar.
I’ve noticed that my four-year-old son, with no prompting, picked up on it and uses the wheel to scroll. I’m guessing that he doesn’t even know that he could click on the scrollbar to do the same thing. He would probably put the mouse through the monitor if he was presented with a wheel-less mouse.
I didn’t think so until the one on my home mouse broke.
I thought this was what happened to my new cordless Logitech mouse, but it turns tout the “click” on this mouse can be disabled (and re-enabled) by pushing down on the wheel. I prefer it with the click though.
As for how much I use it - I use it heavily if I have it, but it doesn’t bother me at all if I’m on a computer that doesn’t have it. My office desktop has a trackball with no scroll wheel and I never miss it.