I'm looking for characters (preferably protagonists) which are suffering with some kind of curse.
It doesn't have to be something which is causing danger of death.
After all, one of my favorite tormented character in videogames is The Nameless One, from Planescape.
Is there any other character that comes close to him?

I'm not sure about the exact nature of the term cursed here but I'll throw out Shadowman and EVERYONE in the entire LOK series.

The first game that comes to mind is "Curse of the Azure Bonds", where all six player characters are cursed (with the azure bonds, naturally) and the entire plot revolves around removing this curse.

Simon Belmont in Castlevania II.

Larry. At least when I'm playing. I mean- he's got me in charge of getting him a girl. If that's not being cursed then I don't know what is.

Probably not what you're looking for, but TOME has a Cursed class: http://te4.org/wiki/Cursed

Well then, I guess you can judge a book by it's cover? :P

Shinobi in the PS2 entry.

Gabriel Knight 2 is pretty good at building up the tension about the curse... highly recommended

Nvm.

The guy from The Suffering, I don't think it's called a curse but it kind of is.

Frog from Chrono Trigger comes to mind.

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... never played a game that was fond of it.

Dragon Quest 8, but you don't find out until the postgame.

Edit: One could also look at SaGa Frontier 2, where one of the main characters, Gustave, has what I would classify as a disability; in a common magic setting, he is unable to use magic, and that fact is crucially important to the plot.