I respectfully disagree. Her voice is OK but not all that exceptional to any degree. Among her contemporaries, I think Sara McLaughlin, Tori Amos and Amy Lee of Evanesance all have much more exceptional voices and much more talent as performers and as original song writers.
Sinead O'Connor’s main claim to fame was making a really good cover and video of a song written by Prince – “Nothing Compares to U” and tearing up a picture of the Pope on SNL. Outside of those, what is she know for? Her crazy antics and certainly not for her music.
We'll have to disagree then, although I will cede you that there are better original songwriters. She may be "best known" for her cover of a Prince song, but I really don't want to go down the path of judging music by what's "best known" or most popular. A lot of her more obscure stuff that never got any radio play is exceptional. Her acapella song I Do Not Want What I Haven't Got is an excellent showcase for her voice, and I can think of few songs more haunting than her cover of Scarlet Ribbons, to say nothing of her performances with the Chieftains and other Celtic ensembles.
Certainly, she is "best known" for one song, and a few public antics, but IMHO, a fair judgment or assessment of anybody should consist of an examination of a greater body of their deeds and works.