I think if Giles didn't exist it would be necessary to invent him.
Giles is probably the most important of the things working in the background of Buffy that make the series special.
He provides the moral compass to the series and makes sense of what are often nonsensical situations.
If you don't have that you wind up with something like "Birds of Prey", where there's a lot of cool stuff to look at on the surface, but overall it's silly and it doesn't seem to be going anywhere.
Giles is important even when he's not around. Do you remember at the end of First Date when the Scoobies are just hanging around goofing and joking about sexual orientation. That was fun. I was enjoying it, then Giles butted in and forced everyone to see the seriousness of their overall situation,
OK... I didn't understand the importance of a scene like that to the overall gestalt of Buffy until I saw the next episode, Get It Done. This episode was Gilesless. Fast forward to the Buffy lecture scene after she buries the girl in her backyard.
I agree with everyone who found that lecture scene a little tiresome and fragmented, but when you put it together with the Giles admonishment from the previous episode, you see where Buffy's coming from, and even though she's a big pain in the ass in that scene, you recognize the importance of what she has to say. I submit to you that the aura of Giles is present in your subconscious when you view that scene, even if you didn't notice the connection consciously.
When Giles leaves the series for too long you have chaos. You have Season 6. Does everyone remember the feeling you had at the end of Two To Go when Giles stood there in the doorway of the Magic Box dressed in a trenchcoat and not wearing his glasses. It was like "Ok...everything's going to be alright now. Daddy's home, and he's pissed".
But the question of this Poll concerned the importance of the Giles/Buffy relationship. Hell ya it's important, but first you have to take into account the general underlying importance of Giles.
Also don't you just love the chemistry Sarah Michelle Gellar, and Anthony Stewart head have together as actors. Watch their faces and they're saying stuff that isn't even in the script.