I wasn't cataloging them in my head, but I can't image "Roxane", "Message in a Bottle" or "Walking on the Moon" without guitars. The bass is obviously important in those songs, but they'd sound empty without the guitar.
Well, if you just take guitar out of these songs, they'll be empty, but in many cases it could be something other than a guitar, I think.
It's somewhat akin to when you listen to isolated tracks performed by great drummers - there are ghost notes, dynamics, all that stuff that you can easily miss when you listen to the whole mix. They are essential, yes, in that they differentiate great mix from a good or a mediocre one, but they're there in the background, kind of hidden.
So I guess that's what I meant with regard to relative importance of guitars in different genres.