No. Apple's latest monitor connection looks pretty close to DVI, but it won't work. I believe there are converters available, but I'm not 100% positive.

The apple connector is referred to as ADC... that should help you in your search for converters.
 
Last time I looked though, the converters were really expensive - it would probably be better to pay a little premium to get a really nice PC LCD display with native DVI.

I gather that you're enquiring about DVI connectivity, so I can't really comment on that. However, it IS possible to use an Apple analogue CRT monitor on a PC (15-pin sub D) - so analogue operation - as I do that on my second PC.
 
I tried for ages to get a small PC-to-Apple video cable adaptor in the UK but had to give up in the end. I then quickly found a supplier of such an adapter in Florida and, for $15 including postage, got one. Works fine. Nothing to do with digital, though.

Converters can be had all over the place, but they aren't cheap. I've seen some as high as $400USD. Apple actually makes one themselves they sell for $99USD. They claim it only works on PowerBooks and G5s with DVI, but I have it on pretty good authority (my brother) that he uses one with a PC, and it works just fine. The USB plug just enables the 2-port usb hub on the back of the display, and it works on the PC too, at least that's my understanding.
 
http://www.apple.com/displays/adapter.html
 
This one looks like a "swiss army knife" of adapters, but it would probably do the job just fine.
 
http://mac-pro.com/Merchant2/merchant.mvc?Screen=PROD&Product_Code=dviator&Category_Code=cb