I've heard it mentioned before on the forums, and I imagine it would be a pain to setup, but I think it would be great if more NPCs started interacting with you rather than you with them all the time. Even better would be if they bug you about things you bug other NPCs about. The basic way I am envisioning it is to do some spawn points in various locations (cities, taverns, stores, inns, wilderness, etc) like MCA or Starfire's NPC Additions, but have these NPCs set to force greet the PC when they approach them. Some different types of NPCs that could be included to keep things diverse, with a nice considerable chance to have no one spawn in these locations as well (each location should probably get a half dozen NPCs or so to keep things from getting immediately repetitive). As for things that could be discussed in these:
Begging: The NPC is poor and begging the PC for money (granted the PC doesn't do this a lot, but can enough).
Rumors: The NPC asks the PC about the latest rumors. Could possibly set this up so the player can give some different responses based on different conditions currently in the game.
Services: Similar to the rumors option, but could be specific to locations so the PC can guide the NPC around town.
Advice: Possibly just offer up a few different options for the PC to be able to give out to the NPC asking for the assistance.
Freelancer: Now the supposed "great cover class" of Morrowind can exist - Mercs offering their services during a set time period for money. Very basic companions, non-leveling, but basic warp and such and companion share.
There are probably a number of other things that could be done with this as well, but it could go a long way to making the player feel more "at home" running around doing these same actions with NPCs all the time if NPCs occasionally do it to them too.
As I mentioned though, it should be carefully balanced so that it doesn't happen all the time (as that would spoil the effect by making it less random and too standard, plus it could get annoying if it happens too often).
IMHO, spawn points and specific NPCs would not be the best way to do this - there will still be a glaring difference between "talk to me" NPCs and "vanilla" NPCs. There is a way to implement this feature (and a plethora of others) to vanilla NPCs and still manage to keep it "generic."
The way to do this is in the dialogue. In the voice files, you can attach a script to an entry that might be spoken (on greeting) by random, and launches a script instead. This script will automatically apply to that NPC and can simply launch a ForceGreeting command. Use the script to apply some temporary conditions to use as variables, then have dialogue entries in Greeting 1 for whatever the NPC wants to say.
You can use the script and dialogue filtering to assure only certain kinds of generic NPCs open dialogue. When an NPC fires a script on themselves from a voice clip, then that NPC is subject to almost the entire spectrum of Morrowind code. This opens seemingly limitless opportunities.
--Edit -Vtastek has the right idea. Didn't see that till now.