I always think of "Self esteem" when I think of "offspring" even though it seems like other songs like "why don't you get a job" are the ones most people know them for.
Oh, and with Audioslave I think of Like a Stone.
Seether is "Fine again". Coldplay is "clocks".
And Hoobastank is... surprisingly is not "Because of you" but "Running away", which is the first song from them that I heard and hooked me.
I agree, Gianni. I think it is nice to get immersed into what a group has to offer, after all if we already liked one, there may be more gems within. BoB Dylan, The Eagles, Off Spring, Green Day, Cold Play, Linkin Park, etc.
However, I don't mind the fact that there will be a first song that will come to our heads upon hearing a name. It doesn't mean it is all we know them from, simply the association we make.
Exceptions in my case:
Rebecca Black (Friday!) and Justin Bieber (Baby, baby, Oh!) are two people that I only know one song and I don't feel compelled to search more or have been exposed to other themes.
I keep coming with more names and songs, but I'll stop here for now. :]