Karyn
Bordering on the shameful pleasures list... I like Pink, but I'd never buy any albums. I don't "get" that style of dancy girly pop, but having seen her live act on TV (proper live, not studio) I do admire her singing talent. She has a good voice and could go far..
 
More mainstream for the CH I've "got" Rush since about 1980.  I ignored them at first because of Geddy's squeaky voice.  I had a friend that was mad for Rush and just wouldn't shut up about them and kept playing all this weird stuff with sink o'pa cynko out of time drums and a squeaky singer. It wasn't until "Exit, stage left.." that something clicked and the squeaky voice didn't matter (or his voice broke...)

I can relate to your post, Karyn. Sometimes you have to see a band in the right light to appreciate them. Both of these are acts that I initially did not care for, but have since become a fan of. I'd recommend two videos to you, each of which was the turning point for me with regards to these artists.
 
First is Pink's Funhouse Tour concert video. If it doesn't make you a fan you'll at least appreciate what a monster talent she is. I mean, how many people can sing upside-down? Her Zeppelin and Queen covers alone are worth the price of admission.
 
The other recommendation is the Rush documentary "Beyond the Lighted Stage". I was definitely NOT a Rush fan before watching this video - like you, the squeaky voice put me off. The epiphany that turned me into a fan was that the stuff I'd always heard on the radio is not the band's strongest material.

bitflipper
 I mean, how many people can sing upside-down? 

 
 
Now over 1000 shows belting upside-down twice a night... 
 
Just saying. ;)
 
 

Springsteen.  There, I said it.  Geez, I feel freer for it.  Ok, and anything by Stevie Nicks.  That's a voice?  At least Christine McVie had something that could be called "tone". 

Old55
 
I'll start with Fleetwood Mac(the non-blues version).  They may be technically brilliant.  Stevie Nicks may be a great singer, but her voice gets on my nerves for some reason that I can't explain.  

Maybe because it's cloying and somewhat nasal?  I feel exactly the same.  But I don't mind her in the context of Fleetwood Mac.  I do stay far away from here solo stuff, however.

While I think I respect what he was trying to do, I just was never moved in the slightest by Van Morrison's music.  I once had some friends who really liked him, and I heard quite a bit (this was like 40 years ago, by the way).  Just never got it.

Rolling Stones
Grateful Dead
Anything heavy rock

Old55
It's hard to choose just one.  Almost every band that was over-played eventually got on the list.  
... 
I'll start with Fleetwood Mac(the non-blues version).  They may be technically brilliant.  Stevie Nicks may be a great singer, but her voice gets on my nerves for some reason that I can't explain.  
...

The only albums I have by Fleetwood Mac, are the first with "Oh Well", then "Penguin" that has one of my favorite songs (Dreams), and then "Bare Trees". The Stevie Nicks era for me was all about the rich bee and what not, and it was tiresome and boring for me. Never bought or touched those albums!
 
My old roommate that was in the FM station in Santa Barbara, one time got so mad about the number of commercials on his show (Space Pirate Radio) that the whole first hour, he played a song from the big hit album, some 19 times in a row, and each time saying ... here's a song that you're gonna love ... commercial ... and then do it again! 
 
Not my type of woman! I liked Christine a lot more and her voice was not annoying or self-righteous.
 

bapu
Unfunny response: Any suggestions by Pedro.

 
I've always said that if you go down, go down swinging your own tune. You don't need to do covers because you won't be heard. The original gets the credit, you don't! It's like Michael J Fox going nuts on a rock song with a guitar and everyone looks at you like you are an idiot! 
 
Right place, wrong time! as the good doctor said.
 
(ohhh man ... a thread like this gets me juiced up!)

bapu
OK, here's my real response. The band America.

 
Ventura Highway, was my theme song for at least 10 years, like driving between Santa Barbara and LA area for anything, be it a concert, or simply to go to Moby Disk, or the Tower on Sunset, or the Warehouse in Westwood.

UbiquitousBubba
... 
Bob Dylan. I'm told that he's the greatest poet who has ever lived, but let's be honest.
...

 
Because of the internet and the evolution of music and its proliferation, it is hard to now consider Bob an important writer, and poet. However, forget the music, take the words as if you are reading a book, and put it against your top list of American Poets in the last 100 years, and the only one that will stand out might be E. E Cummings. 
 
However, Bob is very much a "reactionary" to the time and place, a lot more than most poetry writers.
 
I don't bother with listening to Bob sing, because he is not a singer, and everyone can do his stuff better. Why are you bothering to look for a singer when there isn't one? He's about the inflection and the acting on his words, which can cut really hard and harsh in the way he says it.
 

UbiquitousBubba
...
Neil Young.

 
Check out the film that was done by Jonathan Demme about him, and his solo concert. He is out of tune many times, but it's a part of the person he is, and what he is singing about is not a "song" that you WANT TO MAKE SURE IS PERFECT, but about his feelings. It takes courage to sing a song about someone in your life, and calling and not getting an answer. It takes courage to sing about Kent State. But no. You want the syrup'y crap songs like Suite **** Two Eyes? That is not what Neil is about!
 
And unlike many other musicians, btw, he manages to stay with it and mix with new folks, and that is something that most of the players his age can't do because they are trying to make a living off their teens that were meaningless save for a nice song about nothing, or flowers in your hair!
 
It's not about the voice or the singing. It's about the "performance" in the theater, when someone gave his heart out to the end ... and all you can say is that the voice screeches. You never heard a word? It needs a screech, because most people did not HEAR it then, and STILL don't.
 
I would like to suggest that you might want to take your DAW knowledge and ability away from these folks. Their work was NOT about the idealistic "perfection" and "design" that you think a song should have. In many cases, it was the "imperfections" that made the piece in the first place, and this is the problem with all these DAWS. 
 
You forget the music itself, and what you are doing!
 
Another person that is very similar to Neil, that also screams, cries and sings his heart out non-stop is the one and only Peter Hammill, and his band Van der Graaf Generator. I much prefer his solo material, it is harder, stronger and intense and sometimes too much so, but it is hard to not appreciate the strength in "H to He", "Godbluff" and "Still Life" though most fans seem to like the other album I do not think is his best. But this is a style, of honesty, heart and feeling, that few Americans will appreciate and it won't get played on the American airwaves, though some songs are unbelievably fabulous! He makes Neil Young look and sound like a child trying to bring out a song, which I think is a very good and apt description of Neil, but in a good way! That wildness counts for something even if you don't like it, or as a parent you try to instill it out of the child!