I've been given a used computer that is better than my own. The new one is a Dell 4600c and my current one is a Dell Dimension 2350. Both currently have 256MB of RAM. I was wondering if I can move the 256MB from the 2350 into the 4600c assuming there are available spots (I haven't opened it yet). Is this possible? Anyone know if these computers use compatible RAM? Thanks.

They both use 184 pin DDR DRAM.  Both of the machines have two slots for memory.

As long as they each have one DIMM then you can move the memory over.  You'll see a huge increase in preformance going from 256 to 512, plus it's one of the easiest upgrades you can do.

Crucial says:

Dell 2350 = DDR PC2100 (266MHz)
Dell 4600C = DDR PC3200 (400MHz)

I would not put the PC2100 memory stick into the 4600C.  it won't kill the hardware, but you're likely to see repeatable errors while trying to run the 4600C on the slower memory.  The errors will basically cause frustration, but they could also corrupt data on the hard drive makeing Windows unbootable at some point or you might lose some data files.  However you can use the PC3200 memory in the Dell 2350 without any problems.

Personally, I'd probably go buy a 512MB of PC3200 and put it in the Dell 4600C and move the PC3200-256MB stick over to the Dell 2350...that way you'll have both! .  Well...ok, I would actually buy 1GB of memory instead of 512MB.