Finally!
I've finally found someone else with the same problem! I have a 17" 2.16GHz Intel Core Duo MacBook Pro from September 2006. It has the ATI Radeon x1600 graphics card, Tiger 10.4.11, and 2GB RAM. All of my firmware, drivers, and software are up to date.
The artifacts started about a year ago. However, when it first started, there weren't lines on the screen. It would be a single pixel, usually pink/purple colored, and when you would drag a window across it the pixel would stay in place relative to its position on the display, but it would "draw" a pink/purple line across whatever part of the window was dragged across it. The "drawn" line would be whatever shape was made by whatever direction you dragged the window... i.e. it was like if you held a pink marker in your hand, pressed the tip of the marker against your desk (keeping your hand still) and then moved a piece of paper beneath it in whatever arbitrary direction.
Those artifacts have since ceased, but worse artifacts are now showing up, very similar to creator2456's artifacts. I will get random horizontal lines on the screen, usually the width of whatever window they happen to be "contained" in. An example can been seen at
http://s147.photobucket.com/albums/r306/CaseyCoffey/?action=view¤t=Picture3.png
In the example above, you can see three distinct black lines in the Firefox window and then a white line crossing the top portion of the desktop. If I scroll in Firefox, the black lines move with the scrolling, as if they're drawn into the web page. They normally disappear when you scroll far enough so that they've scrolled into the non-viewable portion of the window and then return to the original location on the page. In this example, the white line across of the top portion of the desktop has been there since I turned on the MBP today.
The problem is getting worse, too. Very rarely, but more frequently now, I'm seeing not just lines of artifacts but entire rectangular blocks of artifacts. I don't have a screen shot of those, but it's usually a scrambled artifact with diagonal lines.
I also have an external digital 20" display that I connect to the MBP. The artifacts show up there as well.
Finally, to top it all off, my system freezes regularly. It has been getting increasingly worse, and it appears to somehow be related to the video. It's freezing almost daily now, with a hard reset the only way to recover. It usually freezes when (a) the screen saver is active (most notably the "flurry" screen saver) or (b) when minimizing or maximizing something to/from the dock or (c) when the dock is going from shown to hidden or hidden to shown.
I have wiped the system clean and reinstalled OS X twice. It hasn't helped. I've looked everywhere for a solution, but I'm convinced it's a hardware issue, likely the logic board. I'm a big Apple fan, but I am furious that I can spend $2700 on a notebook that is consistently failing two years later with ZERO warranty left on it. A new logic board will run me about $900. I am not happy about this, but hopefully someone has a helpful suggestion!