I've been running my monk character Tyr Infinius all over Morrowind and I have the
screen shots to prove it.
That's one of the more tedious parts of the game actually, all the running around you have to do. Some of the fast travel options in the game (silt strider, boats) help, but there are still just some parts of the map you have to hoof it. The more you travel about, the more likely you are to see one of Morrowind's notorious CTDs (Crash to Desktop). The game was actually more stable before I upgraded my video card, but the increased quality of the graphics was still worth it. I've just got in the habit of using F5 before I fast travel, or enter/exit areas. If the game is going to bail, it usually does it immediately after one of those events. I can also sometimes tell when it is about to do this because of visible graphics artifacts, like missing textures.
I've also been playing around with the morrowind.ini file settings - disabling threading (setting DontThreadLoad=1) seems to make a difference also. You get longer pauses between areas, but fewer of those "loading area" notifications.