I figured it wouldn't hurt to update this old thread with some newer photos and information about my lovely A600 for anyone out there who is still interested in real Amiga computers. Although she is in need of a capacitor replacement and general once-over from an Amiga repairman, Workbench still boots up after a few minutes of power rerouting and shield stabilization. After that it reboots as quick as you would expect.
Thanks to my good friend tone007 my A600 is accelerated beyond all previous expectations. She now sports the bee's knees of expansion boards, the ACA630/30 with 64MB RAM from Individual Computers. I have replaced the old Compact Flash card with a brand new 4GB SanDisk Ultra II CF card, partitioned with two SFS partitions with Workbench 3.1 and several programs, games and utilities installed, and a 1GB HFS partition with MacOS 7.6.1, various programs and 16-colour-compatible games.
Now I can browse the web, including Amiga.org (through Karlos' awesome proxy and new 640-wide option) and play my favourite online multiplayer game, Dynamite, on my cute little A600, as well as playing DOOM and a few other FPSs and CPU-intensive games.
She is protected by a nice fitted dust cover given to me by my good friend fitzsteve, and is connected to my LCD TV via a RGB-S-Video adapter from AmigaManiac.com providing a flicker-free display in all Interlaced modes!
So, here are the pics!
First is an older photo from before I got the ACA630 but after I had put together a really killer 3.1 setup for low-end systems. The CF drive from this is now in my other A600 (whose motherboard was provided by tone007, thanks again!) where it sports the 2MB PCMCIA SRAM card as well for a total of 3MB System RAM. I'd love to get another A603 to bump it up to 4MB, and even one of those upcoming 2MB 020 accelerators.

Here is a newer photo of her running Photoshop 4.0.1 (the final version for 68k) under MacOS 7.6.1. It runs very well and is perfectly usable. I have adjusted it better since this photo so the display fits to the top and bottom of the screen.

And here is a screenshot from my A600's Workbench, browsing Amiga.org and playing a game of Dynamite. Unfortunately I'm only playing against bots these days because hardly anyone ever wants to log in anymore! How could you resist such a fun and customisable online multiplayer Amiga game?

More to come, as I don't really plan on sleeping for a few weeks while I play with my awesome new setup.