Geez, I had to go through a lot to post this....
If your walls are dirty and they are painted with a semigloss, clean and skuff with sandpaper.
it really comes down to what your painting over. Painting over glossy paint, skuff with sandpaper, cleaning wouldn't hurt. Painting over flat paint, you might want to skuff it a little, but probaly don't have to.
me

Thank you fishead and faron. I was hoping to get by with less work...! But so be it, will do.

Everything Faron said, but I also recommend the Dirtex over TSP. Dirtex is safer to use and doesn't require a rinse. TSP will prevent adhesion if not properly rinsed, and rinsed well.

Washing will Dirtex will also degloss the walls which makes the paint adhere better.

Don't skip the primer!

Michael

I didn't wash mine, but I took a swiffer over them and was amazed at how much dust there was. I dust the horizontal surfaces regularly, but didn't realize how much dust stuck to vertical surfaces.

With paint - cleanliness is next to Godliness. Clean the walls - check for residue - tint your primer if you are priming. If you are using flat finish, one finish coat may do the trick for less work. Two finish coats IS best.

Try a wall and see if you like the results. On better way than that!

Have fun!