According to this Wikipedia article for example the AMD Opteron 2389 is designed for registered DDR2 RAM (see the list at the beginning of the list of CPUs).
My question is now: Can I also use classic RAM or does it have to be registered RAM?
Physically, registered and un-buffered (not fully-buffered) DIMMs have the same physical connections and operate in the same manner, although you may experience hardware issues (memory errors). The idea of registered RAM is to provide a memory signal "buffer" (which usually takes 1 clock cycle extra) to drive the output from the memory (instead of directly using the output). This allows for systems to, potentially, increase the maximum memory frequency & capacity, but at the expense of a higher memory latency (as all reads/writes are buffered through an additional set of registers).
This "buffer" is a physical piece of hardware, so it really depends on if your particular motherboard or CPU requires it for proper operation. The CPU itself does have an integrated memory controller, although I see no explicit requirement for registered memory except if you already have some (you may experience timing issues if you try to combine unbuffered and registered RAM modules). The thing is, it depends on your particular hardware (especially how many DIMMs you have).
If indeed the hardware runs with unregistered memory, although you experience memory errors, you should be able to increase your RAM latency, or decrease the memory frequency, to prevent these memory errors from occurring.
May be AMD Opteron 2389 will give better performance with registered DDR2, but whether you can use standard ram or not is more dependent upon the desktop board you will use with it. The board specification will tell you as to which Ram you can use.
In many cases you have the option of using both.