I have a Micro*ahem* IntelliMouse Explorer, and have had the problems described. However, unlike many people here, it seems, I find that under OS 9, not X, the mouse is extremely tempermental, often turning itself off and then on again for no obvious reason, and sometimes turning off completely and not coming back on at all until either a complete restart or I plug it out and back in again.
If dies during certain games (e.g. Starcraft) I lose the functionality of the buttons, so that they all trigger a normal left click, not a proper right click or whatever. The mouse still works fine in the Finder. I believe this is a 'bug' in InputSprocket, which Starcraft uses (the same problem occurs in Quake 3 and Tournie, although generally in them I lose the ability to mouselook too).
Anyway, under OS X the mouse behaves wonderfully. It does rarely die, but only for a second or two, and when it comes back there are no problems such as I've described under OS 9.
Now, it turns out this isn't an uncommon problem with Microsoft optical mouse. If you phone up Microsoft help and describe very generally what's going on, they'll offer to replace your mouse free of charge. Why? It appears all their optical mice *ship* with several very common faults, including easy to break or already broken cables, faulty USB connectors, and generally (and somewhat randomly) bad internal connections. These cause the dead-one-moment-fine-the-next symptoms. Many of my friends have had the problem (probably 75% of them, in fact) within 6 months of buying their mouse. Some of them returned it, while others have managed to fix the various problems by opening 'er up and tweaking things. If the cable is faulty (test it by moving the cable where it enters the mouse to the left and right on a sharp angle. If the mouse reliably dies at a certain point and works again once you straighten the cable, you've got said problem) then you can simply cut about 10cm from the mouse end of the cable, rewire it inside, secure it properly internally with some blue tack or glue or whatever, and it seems after that it works like a dream.
If you have a faulty connector, as I believe I have (in addition to the cable fault), you'll find sometimes, especially with OS X installed, the mouse won't even start up when the system starts. This is especially troublesome if you're trying to select a startup disk (by holding down option at startup). The solution is to generally hit it in frustration, and plug it out and in again until it works. So far that's fixed it each time (the hitting it part is optional, but I recommend it for good measure, and the stress relief
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Microsoft won't announce anywhere that they have these problems, and they seem to still be having them even with brand new ones, but they won't even bother asking questions if you report this problem to them.