You could try taking the trap off, which is to say the U shaped bit underneath. If your sink looks like the one in the photo, you'll need to take off the "pedestal" fascia to reveal the trap and then it's just attached with screw compression fittings.
It's also possible that the trap is either non-existent or mis-installed to render it non-functioning meaning that the smell is actually sewer gas coming up through the drain.
The point of the "trap"--they can be either t or u shaped-- is to keep a water seal to prevent this from happening, but who knows without looking at it what you actually have and whether it's right.
The pipe that extends horizontally from the back of the trap into the wall should also be pitched so that it's lower where it enters the wall outlet than where it's attached to the trap.
This is all very simple basic proceure, but if it freaks you out, call a plumber. Sewer gas is a bad, bad thing that you def. don't want in your house.

Ugh, we deal with this, too. I use a combo of vinegar and baking soda weekly and get in there with one of those long, skinny brushes. I always find black mold- every week! And it smells, almost a little supher-y.

I've never been the one to take care of this problem myself, but I've heard other people mention sending a shot of bleach down the drain, or boiling water, as either should kill whatever is growing in there. But I second splatgirl and suggest taking a gander at the trap.

@The Sweetest, I do the same but it lasts longer, so maybe I use more. I push down a whole box of dry baking soda. Then I quickly pour down a cup of white vinegar. There's a funny kind of explosion that seems to open the pipe fully, improving flow. When one try doesn't finish the job I repeat it, and so far no more than that has been needed to remove odor or partial blockage. It's supposedly safe.

I just spoke to my plumber about all the black in my bathroom sink drain. He said it's not mold but TOOTHPASTE! Apparently, it doesn't fully dissolve and turns black. He recommended flushing the drain periodically with hot water.

i get a sulfury smell - i can't tell if it's the water coming out of the faucet or the drain. because it doesn't smell until the water starts flowing. it's annoying!

As others have mentioned, if you've got a really foul smell, you may have a bad trap. If the trap doesn't stay full of water, sewer gases will come up through it.

@annki, How funny, my washer repairman said that the upredictable deposits on my washloads of drops of what looked like black grease were bits of mildewed detergent buildup. He told me to run a hot water heavy duty wash cycle once a month with just a half cup of white vinegar. The mystery globs stopped happening.

Joan in SB, I have the same exact thing happening to my sink! Do you notice more late at night and first thing in the morning? I have had plumbers tell me that the vent could possibly be cracked allowing the sewer gases to come through the water. I have tried clearing the pipes, and it doesn't seem to help.

This is going to sound disgusting, but here's how I've done it.

A plunger.

Yeah.
Fill the sink up to the overflow, and plunge like mad. With enough force of water and elbow grease, the water comes back up out the overflow and brings with it the disgusting black goo of old toothpaste, hair, shampoo, and whatever else goes down your drain. I typically have to fill the sink a couple of times to get it all, but it's proven an effective method for me.

All of the above, plus boiling water. I had a problem drain in our old house, a no-longer-code T connector, meaning the water had too move laterally for a couple of feet before going down. I bought a thrift store electric tea kettle just to keep that drain moving. One or two pots of boiling water cleared things up every time, and no damage to the pipes.

I actually had a really bad smell come from my water spouts *after* I had decided to give them a good cleaning and soak them in bleach water. Happened to both a shower head and a sink filter. It really smelled deathly - unlike normal mold or mildew - and I have since decided it was because I killed too much. There were probably organisms living in there (NYC water is filled with microscopic crustaceans - so much so it was actually declared un-kosher) that helped maintain a stasis, and I had to allow it to return to equilibrium.

@bodicegoddess, Yes, a plunger can work well and be safer than some chemicals. They make them for sinks as well as for toilets. The two kinds are differently shaped.

I bought one of those "As Seen On TV" drain un-cloggers. It's a thick wire with kind of a mascara end on it, and you feed it down into the drain and kind of twirl it. It brings up a lot of goo and gunk. Must be toothpaste and stuff reported by other commenters. This may help?

Thanks to everyone for the suggestions. My boyfriend confirms that it is not the trap and it is not the drain (I've put lots of baking soda, vinegar and boiling water down there). It actually seems to be an area to the sides of the overflow. I'm thinking a bottle brush sort of thing might do the trick but am very happy to have your thoughts. That mildew smell is bad!

I resolved my similar issue with dentures tablets and the shower head.
My sink is next to the shower where, fortunately for me, the head is not fixed on the wall.
So first I used the shower with hot water and the strongest jet to wet the surfaces in the overflow so that the tablets bits could than stick on it and to soak the smelly bits there, then I crumbled some tablets and with a bit of patience I throw them in the overflow. I waited few hours and than I used the shower head again and all the smelly bits fell off and went down the drain.
No more smelly bathroom! :0)

I had the same problem for a temporary period. I cleaned the sink with Ajax powder and hot water twice per day and poured baking soda down the drain every night so it could work on the bacteria overnight. It corrected itself in about 72 hours.