Why not ask the landlord for a can of the paint and repaint it? You can't help smudges that result as "a few years" of occupancy! Dirt happens!

You said that the desk hasn't been moved in a few years so I am guessing that you have been in that rental for quite a while.

Given the time frame, it is perfectly normal to accumulate wear and tear on the wall. Just ask your landlord if it would be ok to paint to freshen things up since it has been so long between painting. I am sure he would not object.

Have you tried the Mr.Clean Magic Erasers. I had smudges when I was moving out of my last apartment and these took care of them with no problem. Also, if you've been in your apartment for a while - say 5 years or more - you might just ask your landlord to repaint.

Can you not discuss this with the landlord? S/he will need to paint it when you leave anyways (likely paid for out of your damage deposit), so s/he may be willing to let you paint it now as well, as long as you use approved paints/colors

I second the Magic Eraser suggestion. Try it before asking your landlord about painting, as others have suggested. The thing does do wonders.

Oh honey, Mr. Clean Magic Erasers! They are a renters best pal.

Be careful because they actually gently resurface the paint. Only scrub as hard as you need to, but i had identical smudges in my last rental and the sponge thingie fixed it all.

I'm just guessing but the last tenants probably had a desk there and put thier feet up all the time.

Ideally you would wash and paint once they got that bad, but you need a cheap easy fix.

I think I read somewhere that in NYC, landlords are obligated to repaint rental apartments every three years if the tenant does not move, as well as when tenants change. If you don't want to do that, I would definitely just ask the super or management to borrow a can of the paint for a day and do all of your touch ups. I do this about every 6 months and it's never an issue.

Have you tried washing the wall (rag and some hot, sudsy water)? If you have and it didn't come off, can't you just get some paint chips, match the colour, then just paint over that area?

Generally I've found that landlords welcome your efforts to maintain your apartment. It gives them less work when you move out. Don't be afraid to ask. The worst he can say is no.

Be careful with the magic erasers. They can work wonders but do not work well on flat and some eggshell paints. It will take the paint right off. So test it out first.

Baking soda or Comet with some elbow grease.

Um, the "no painting clause" doesn't mean no "touch up painting." Get the paint from the landlord as mentioned above, or just match it as closely as possible.

But have you tried soap and water?

At work, we have white walls and white desks. When we first renovated, the heel of my shoe hit the wall and made a black smudge. I used an old fashion eraser and the smudges came right off. It works well on matte finish paint as well as my metal white file drawers.

You could get a large piece of MDF, wall paper it and lean it against the wall.

Magic Eraser. No question.

Everyone else already addressed the smudge, so I'll just go with the "what if none of those worked?" assumption:

Lean a large framed mirror against the wall in front of the smudge. I'm not talking about a $400 mirror from Pottery Barn but a much cheaper one from Ikea or Surprise Surprise or something like that.

And I believe there's an electric outlet around the spot, so you can but a colored bulb behind the mirror to give it an interest glow at night.

...so you can PUT [not "but"] a colored bulb...

I have a red bulb behind a leaning mirror that i turn on for parties.

No matter what you do the dirt will not go away.

Mr. Clean Magic Erasers worked for me.

Is it a good spot for a plant?

what about wall decals?

Grab up some framed artwork and lean it against the wall.

ditto the magic eraser. Although, if you rub too hard, it will take off some of the paint's sheen...depending on if it's flat or semi gloss.

But hey, a little less sheen in one spot is better than a smudge.

If the magic eraser doesn't work, shaving cream cleans walls really well. Not the gel kind of shaving cream, it has to be the kind that comes out of the can foamy. My walls had all kinds of dirt on them from my kids and the shaving cream and a wet rag cleaned all of it off.

If cleaning it off doesn't work, you could make a large piece of art work and having it leaning against the wall. A floor to ceiling wall hanging would work as well.

Magic Eraser.

This is kind of a dumb question maybe, but are you sure it's a smudge and not mold? I'm not questioning your intelligence....just putting it out there in case you haven't considered. I can't tell from the pic. I had mold grow once behind a dresser I hadn't moved in awhile from condensation on the window/wall. THAT is something a landlord should definitely deal with.

By law the landlord has to paint/offer to paint the apt. It sounds like your time has come.

The landlord is required to paint.

many people have offered you very sensible advice about cleaning tips and landlord obligations. I hope that works for you, but what about adding some new beauty to the space? I reccommend checking out some vinyl grafics. You can get some really great ones on etsy and lots of paint stores are starting to stock diy kits. Now that would add some spark to your room! Plus, they peel right off and they can be moved around whenever you want! (like when you move out...)

How about cleaning it? If that doesn't work, lean a nice piece of artwork up against the wall.