Output from a show version on my pet Cisco ASA 5505:
Hardware: ASA5505, 256 MB RAM, CPU Geode 500 MHz Internal ATA Compact Flash, 0MB BIOS Flash M50FW080 @ 0xfff00000, 1024KB
So the ASA 5505 shipped with 256 MB RAM. Upgrading the Compact Flash card last week gave me the chance to have a quick shufti inside the chassis. There’s a single slot for a stick of RAM.

The original RAM is a stick of 184-pin SMART brand RAM which I can upgrade myself. I have lots of older RAM carefully pack-ratted away in a Wall-E-esque fashion, stuff that I’ve swapped out when upgrading other machines. Some of the stuff is bordering on antique, but I like to think I am less a-very-special-episode-of-Hoarders, and more why-do-you-collect-commemorative-NASCAR-china-plates.
A cursory snuffle through the search engines tells me the 5505 will probably take a stick of 184-pin 400MHz DDR RAM. Folks on the Interwebs report installing various brands of RAM in the ASA. Seems a bit hit-or-miss, though.
I have several sticks that might suit and I try them one at a time. The ASA is not happy with a stick of Kingston ValueRAM KVR400X64C3A/512 2.6V. All the green link lights at the rear flash on and off repeatedly like an ’80s disco.

The link lights at the front of the unit are flashing on and off as well, and the STATUS light is amber. Nothing comes up on my SecureCRT console.

And then, success on the second try! A stick of Nanya Super Elixir M1U51264DS8HC3G-5T, pulled from a Mac Mini when I did a RAM upgrade on it a while back.
After booting up, my ASA coughs up this result when I run a show version
Hardware: ASA5505, 512 MB RAM, CPU Geode 500 MHz Internal ATA Compact Flash, 0MB BIOS Flash M50FW080 @ 0xfff00000, 1024KB
My pet ASA recognizes the 512MB RAM. Good little ASA, time for walkies!
Additional Information:
Show version command in the Cisco ASA 8.4 Command Reference.