Feel free to add any that I may have forgotten.  :)

U2
The Cranberries
Van Morrison
Sinead O'Connor
Oasis
Baltimora
Gilbert O'Sullivan
Enya
Thin Lizzy
Chris DeBurgh

U2 Some of their songs bore me, but they have good ones in there too.
The Cranberries "Zombie" is terrible.  "Linger" is boring.  "Dreams" has that awful Tarzan-yell ending which lasts for about a minute.  So, yeah, I don't really like them!
Van Morrison He's okay
Sinead O'Connor Nah
Oasis Haven't heard a whole lot by them, but they're okay from what I know
Baltimora Never heard
Gilbert O'Sullivan Haven't heard much, if anything, by him
Enya Just not my style of music really.  Some of that stuff is relaxing, I must admit.
Thin Lizzy Nahh.
Chris DeBurgh OMG, NO!

U2  an excellent band that had its highs and lows...
The Cranberries  an annoying band thats alright
Van Morrison  Ive said it many times, but Ill say it again, Van Morrison is god......
Sinead O'Connor   theres nothing compares 2 U and then theres crap
Oasis  their Beatles Ripoffs, but they do it so well
Baltimora:???
Gilbert O'Sullivan  ah, a one hit wonder singer songwriter
Enya  I hate her
Thin Lizzy  I love thin Lizzy...they had some incredably geat songs
Chris DeBurgh  another one hit wonder

U2   5 for their early stuff, a lesser score for the later efforts
The Cranberries   3.5
Van Morrison   4
Sinead O'Connor   3.5 - okay but boring pretty quickly
Oasis   3 - have never been able to get into Oasis
Baltimora   True ?  The mob that sings "Tarzan Boy" ?  :o  On the basis of it being the only song of theirs I know, 4.5 !
Gilbert O'Sullivan   Fair Dinkum !  :D  I suppose the name was a giveaway!  4.5
Enya   3.5
Thin Lizzy   4
Chris DeBurgh   3.5 - Would have been higher except he tripped himself up with "Lady In Red"  ::)

;D

Artists from the Emerald Isle. eh? Let's have a look...

U2 - the band automatically screams 'pretentious' to me...I'm not disputing they've made an important contribution to rock as a whole, but it's not as important as some make it out to be...'Pride' was their peak...

The Cranberries - 90's group, so not much known of 'em! Did like 'Linger' at the time...

Van Morrison - same credentials as U2, not a total fan but I did like his early RnB efforts with Them...solo-wise, probably the out-of-character 'Brown-Eyed Girl' is his best (and most well-known...)

Sinead O'Connor - dear ol' cheerful Sinead...! Did make some critically well-received stuff, but will forever be associated with 'Nothing Compares...', which does tend to grate...she's apparently heavily involved in religion now...

Oasis - not entirely sure of their ancestry, but I think the group's origins are English (Manchester, to be precise)...the thing with Oasis is, you either get them or you don't...sadly, I don't...tedious group...

Baltimora - the obligatory OHW with the superb 'Tarzan Boy'...sadly, no longer with us...

Gilbert O'Sullivan - despite his early gimmick (dressing up in ill-fitting shirts and short trousers!), he did compose some enjoyable material - he was sadly screwed by his management in the mid-70's, and couldn't really kick-start his career again after it...rarely seen or heard nowadays...

Enya - pleasant enough material, but does become tiresome after a while...'Orinoco Flow' being about the best...

Thin Lizzy - one of the first bona-fide Irish rock groups who made some terrific material...I still can't resist getting the air-guitar out for the intro of 'Whiskey In The Jar'...Lynott was one of rock's greatest showmen until he succumbed to his excesses...

Chris De Burgh - not sure where this guy's ancestry lies either...various references say he was born in Ireland, Jersey, Argentina...he did make some good stuff early in his long career, but immediately blew it all with the awful 'Lady In Red'...

Others worthy of a mention...

The Boomtown Rats - almost-legendary Irish 'punk' group
The Pogues - almost-legendary Irish 'drunk' group
The Dubliners - totally-legendary Irish 'permanently drunk' group, who could even out-drink the Pogues...!
The Bachelors - ever-smiling trio who updated old standards

and not forgetting...
Val Doonican - (the man with the most unfortunate initials!)Irish version of Perry Como with his 'relaxed' style, comfy pullovers, rocking chair and long-running TV show...

U2 ... 3.5
The Cranberries ... 3
Van Morrison ... 4.5
Sinead O'Connor ... 3 for "Nothing Compares To You"
Oasis ... 4 I really like "Wonderwall"
Baltimora ... unknown
Gilbert O'Sullivan ... 4 loved his stuff
Enya ... 2 nuh
Thin Lizzy ... 3
Chris DeBurgh ... 1 yuk

I'll add:
The Corrs ... 3
Clannad ... 4

U2-4 (Had to take off for the techno stuff)
The Cranberries-3.5
Van Morrison-4
Sinead O'Connor-2.5
Oasis-4
Baltimora-1.5
Gilbert O'Sullivan-2
Enya-3.5
Thin Lizzy-4.5
Chris DeBurgh-4

Oasis are from Manchester ::)

Therapy?
Ash

U2
Oddly enough. I didn't care for their old stuff (apart from Angel of Harlem). I'm more into 'Stuck in a moment' (this is one of the few songs that I listen to the lyrics), 'The Sweetest thing' and 'Beautiful day' - 4
The Cranberries
Nah not for me. 'Linger' irritated me - 1
Van Morrison
Best known for 'Brown eyed girl' and the other one. Not keen on him or his music but like that one hit - 2
Sinead O'Connor
Liked 'Mandinka' (despite an irritating chorus) and 'Nothing compares 2U' (written by Prince himself). Well known for ripping up a picture of The Pope - 3
Oasis
I thought they were from Manchester. They certainly have the accent. Only like 'Whatever' and 'She's Electric'. They are the kings of recycling their old music to make it sound new. I keep thinking 'I'm sure I've heard that new hit before . . .' 3
Baltimora
One hit wonder Jimmy McShane does a cracking song. Tarzan calls are a bit annoying but good. Yeah shame he died in 1990 or thereabouts - 4
Enya
I could never hear what she was singing. However I did like 'Orinnoco Flow' and 'Anywhere is' - 3
Thin Lizzy
My dad loved this group. I know 'Boys are back in town' and the like but I preferred 'Out in the fields' - 3
Chris DeBurgh
I don't mind 'Lady in Red'. I prefer 'High on emotion' - 3

As for The Pogues I only liked their Christmas hit with Kirsty Maccoll 'Fairytale in New York'. I think the lead singer sings a lot like Bob Geldof.

Talking of Bob Geldof, I loved his 'Great song of indifference'. I even remember the video where he was smart to start and then as the song progressed, he started to become more dishevelled.

U2  Very good at their beginning but I didn't care for them much after The Joshua Tree.
The Cranberries  Okay.
Van Morrison  Very good, especially "Brown Eyed Girl"
Sinead O'Connor  Never cared for her.
Oasis  Okay...I like "Champagne Supernova".
Baltimora  Love the song "Tarzan Boy"!  ;D
Gilbert O'Sullivan  Excellent!
Enya  Excellent when I'm in the mood for 'New Age' music.
Thin Lizzy  I only know one song by them and they were okay.
Chris DeBurgh  Good.

The Boomtown Rats  Good.
Clannad  Excellent band, and the family of Enya.  :D

U2- 4
The Cranberries- 1
Van  Morrison- 3
Sinead O'Connor- ???
Oasis- ???
Baltimora- ???
Gilbert O'Sullivan- ???
Enya- 2 (relaxing at times)
Thin Lizzy- 4.5
Chris Deburgh- ???