A couple of possibilities...
We have two Droids in our house and they both get fairly warm when talking on calls. At first I thought it was just because I was holding it near my ear. But then realized it was a lot warmer than it should be normally. We live in a spot where our signal is usually weak. So what Hazydave says about the cell tower telling your phone to boost the signal makes sense.
On any call, you're using more power in the "phone" part of the phone than you ordinarily would. Any time the phone is in standby mode (eg, awaiting a call), it "pings" the cell tower every so often, just to stay active... if the tower doesn't get a regular ping, it assumes you've moved on to a different tower. But this is not sustained transmission.
When you're talking, of course, you are transmitting any time you talk, up to at least 1/2 Watt's worth of power (most handsets peak between 1/2W and 1W of output power, the legal limit on most phone transmissions is 3W, but that's not usually something a handheld would do).
However, I have never had a cell phone warm up like this; and they have all received weak signals. Usually, the battery runs down quicker trying to stay in touch with a tower.
So I wonder if anyone else's Droid heats up because of a weak signal and also while talking. Almost every one else on this thread says their's heats up when using the browser.
I think part of the heating is simply that it's made noticable.. the DROID case design assures that the heat sinks to the external case, rather than perhaps being buried in the phone. This is probably necessary to prevent overheating, because the DROID has so many different ways to get hot. The other radios, not likely... Wifi is probably limited to 100mW or less, Bluetooth more like 1mW (most phones are "class 3" Bluetooth devices, good for only about 10m range, so they don't need higher power).
But the applications processor is another story. This contains the 550MHz ARM Cortex CPU, the PowerVR 3D GPU, a 16-bit digital signal processor, additional dedicated processors for video and image processing. When this part is working hard, there's going to be lots of heat, too. Regular phones have very basic application processors, not much need for heat management.
The other aspect this the thin body... all that stuff is in the keyboard/battery half of the phone, which really make the works of this phone crazy-thin. As I recall, my old RAZR could rise a bit in temperature while talking, too... and it was both thin and metal-cased. Ok, and Motorola, but I don't think "hot" phones are particular to Motorola (in fact, they've been looking for a "hot" phone since the RAZR... by all accounts, the DROID is that phone -- over a million sold by years' end, they estimate).