Nope. Computers aren't fast enough yet :p
Nowadays it's even hard to know how a pixel got to the monitor from your RAM in the first place, with the massive amount of knowledge needed and countless layers in between.
Just the datasheet of a memory controller is many times longer than the few pages needed for the asm instruction set and simple schematics of those times. Not to mention the M or G number of transistors on modern chips :)
OTOH, I know a few folks who work with all kinds of micros. Once these folks were trying to interface a SD card reader with a tiny LCD screen that had an onboard processor. They had (had to have, in fact) low-level access to the card reader. You had to know the ins and outs of whatever filesystem the SD card was formatted with because you only had raw access to the card. As in, you could go to an address on the card and do something to the bytes stored there, and that's it. After diddling the card reader interface for a while, they eventually figured out how to get data on the card, but there was a problem: sometimes the card reader wouldn't write the data to the card at all. After trying to pinpoint and fix the issue in code, an entire night of hacking later, the problem turned out to be a faulty power adapter.
It was a fun night. One that a "modern" computer couldn't afford you.
I've played around with machine code monitors on C64 emulators, and I'd love to have something like this on a microcontroller today. (Perhaps a machine code monitor on a calculator?) I don't know of anything like this.
The Maker Shed sells a 4-bit microcomputer trainer from Japan. It has a hexadecimal keypad, 1 7-segment LED display, some other lights and a speaker.
You could also go to eBay or a swap meet and buy an old microcomputer.
http://www.brielcomputers.com/
http://www.makershed.com/ProductDetails.asp?ProductCode=MKGK...
I am currently working on an atmega project and have hopes of bringing such a "self-hosted" programming environment to the device, which I'll post to HN when I get it working.
And no, it hasn't damaged my brain, I think.
On the other hand, if you don't mind things being fast as well as simple, there are dead-simple hobby OSes out there for exactly this sort of tinkering: http://news.ycombinator.com/item?id=1088617
I do remember the fun of PEEKing and POKEing with my TRS-80...