Officialy, no. However, this depends on the creativity (or sadism) of your DM.

The Ring of Sustenance has the following description:

Ring of Sustenance -

This ring continually provides its wearer with life-sustaining nourishment. The ring also refreshes the body and mind, so that its wearer needs only sleep 2 hours per day to gain the benefit of 8 hours of sleep. The ring must be worn for a full week before it begins to work. If it is removed, the owner must wear it for another week to reattune it to himself.

That is all. No negative effects are explicitly listed.

Note that if the ring is removed, it has to be reattuned, which is a week-long process. Therefore, a dispel effect, which would suppress the ring for a short amount of time, may count as removal for these purposes.

Historically speaking, the ring was coveted for the same reason that permanent sources of light were coveted. In older versions of the game, encumbrance was religiously tracked (gold pieces, anyone?), as was light sources, distance of visibility, and area of illumination, and your food supplies (and there were encounters back then specifically designed to ruin your food, and thus place you at risk).

The infamous previous-edition ability of infra-vision allowed monsters (and a few playable PC races) to see in the dark, and track via heat-signatures and/or heat-footprints. However, monsters always had a greater range than any PC playable race. Also, light sources gave your position away.

This was back in the days when players were punished for doing logical things or for forgetting to state that they were doing logical and/or common sense things.

• Carrying a light source? Monsters can see you now, and will subsequently ambush you.
• You can see in the dark? Well, the monsters can see further, so there.
• Didn't carry enough food? Oh, too bad, you get to starve to death in the dungeon. Or risk eating this questionable jello-like substance you found in the dungeon. (It's poisonous, or it's actually a baby slime monster playing dead)
• Oh, look at that, your food was soaked/poisoned/burnt/disintegrated/eaten/other random event Guess you'll die of starvation down here, unless you'd like to try the local delicacy of jello? It even comes in green.
• Ran out of torches? Guess you get to stumble around in the dark. Oh, and since you can't see, let me take away the map you've been painstakingly making this entire time.
• Picked up a duck (insert any other random seemingly innocent object/creature) in a dungeon? Well, you should have known better than to touch a duck (or insert any other random seemingly innocent object/creature) in a dungeon.

Keep in mind, this was back in the day when Gygaxian game design ruled, and sudden-death, choose-your-death, wish-a-death, insta-kill, save-or-die, and never-mind-just-die tricks, traps, and encounters were common, ala Fafhrd/Conan style.

So the purpose of the Ring of Sustenance was to remove the food portion of this inventory-sadism from the equation. Some may even get my various famous adventure and game references from the menus of death and discomfort listed above.

Having commented on all of this, I will paint one possible negative scenario of having a Ring of Sustenance, which is also a famous reference, for those who have read the rather disturbing source in question.

Imagine if you will, being the victim of a cave/building collapse. Your limbs are pinned, but not crushed. You can still breath.

You are in the dark.

Alone.

You can't move your fingers, so you can't take off the ring.

Hours pass.

You can only welcome the oblivion of unconsciousness for 2 hours out of every 24, because of the blasted ring.

Time ticks by slowly... excruciatingly.

A drop of water can be heard periodically.

Drip.

Pause.

Drop.

You can't drink it, but you can hear it.

Hour. After. Hour. The memory of the taste of water torments you, even though you don't feel thirsty.

Days pass.

No one knows where you are.

No one comes.

Weeks pass.

Then months.

Then years....

You can't die, all because of that cursed ring. You slowly go insane. All because of that ring.