I replaced my fan once when it completely failed. The new one has been fine for a while, but these past few weeks it has gotten a bit noisy. Should I replace it again preemptively? I mean, is it the sign of imminent fan failure, or can fans go on like this (a bit noisy) for a long time? (The last time it failed, it just stopped working; there was no noise or other clue that would lead me to believe it's on its way out.) TIA.

Noisy fans can run for a day or a year, or even longer.
I would get a spare one now, just in case, and wait for the one in your R61 to fail.
OTOH, you can now buy just the fan itself and reuse the rest of the cooling 'body'.
e.g.: http://www.ebay.com/itm/IBM-Lenovo-R61- ... 0676286418
Check your current fan/HMM for proper part number.

Thanks, RBS (for the link, too)!

Ah, a few more questions, RBS, please. Re: the fan only option (I can't remember how it was because it didn't apply when I changed the unit), but is that fan in the ebay ad held in to the housing with reusable screws or with rivets? Also, the only reason I would order the fan only and not the entire component would be if it was not necessary to actually remove the entire component to replace the fan. Otherwise, if removal of the whole thing was anyway necessary, I would order the entire component, as I did the first time the fan failed. Is removal of the entire fan/heatsink component necessary to replace the ebay fan only, or does it screw out and back in easily without removal of the unit, rivets, thermal paste, etc.?

You'll still need to take the whole unit out, but you could save by buying just the fan.
If money is no object, by all means get the whole unit. OEM is not cheap though!

Just discovered I have you a wrong link, just the fan: http://www.ebay.com/itm/NEW-IBM-Thinkpa ... 0838231479
Price ca. $12.- (check the part number resp. the fan model/name on your current cooler).

Thanks again, RBS. I'll think about it. Though I'm tempted, because the fan in the ad is so cheap, I just like how the OEM fan I got (the second fan IBM sent me -- the first one it sent me was defective, probably used) came with the exact required amount of thermal paste already applied to it. The reason I say the first one IBM sent me was used or a refurb is because it didn't work and it didn't come with the thermal paste. Applying the thermal paste properly is something I would do wrong.

An update:

Did order a replacement fan with hardware from IBM and replaced it. It works great. But this time I'll save the old component and order a replacement muffin fan for it.