I personally WISH SF had a good story structure, but to be honest, its actually something they've been vary weak with.  Back stories keep getting re-written, characters keep zombifying (coming back from the dead *cough*gen*cough*gouken*cough*dictator*cough*) with at times hard to believe at other times absolutely no explanation as to how or why they're still alive, and often their games have only 10 seconds, or about a single paragraph per character of actual story, not nearly enough time to really tell anything meaningful, and often only causing more questions rather then answering anything at all.  Seriously, what the heck was up with balrogs ending for instance?

Maybe their story is better then say, king of fighters, but games like blazblue and guilty gear blow SF away when it comes to story telling.  The story mode is so good in blazblue it pretty much single handedly jusified the purcahse for me.  SC4s story was a bit of a let down, but in the past they're games also had very deep and interesting stories which had me constantly coming back for more.

I for one LOVE a good story in fighters, probably more then trials or vs play though both can be enjoyable as well (didn't get SSF2T:HDR for the story for instance), and more often then not fighters with good, long, developed stories tend to instantly get my purchase while those with out any story (*cough*King of Fighters 12*cough*) tend to only even get played by me if set up for trial in a best buy.

Anyway, I hope Super 4 dramatically improves the story telling, but honestly, I'm not holding my breath.  If the price is right theres a good chance I'll be buying the game regardless, but if SF was known for having a deep story mode I'd probably be much more likely to make it an auto-purchase.

Gen never died >_>

He SHOULD be dead, it's more of a "how has he not died yet?" than a "back from the dead".

Gouken's some sort of clone of the original apparently.

I think SF had a great story until 4 and now its very hard to put it together especially with the lame endings

I think they put more effort into SFIV endings and storyline than lets say SFIII. Whether or not you like where they are taking the story is preference though. In SFIII, they drew a few fancy pictures and put them together. With this, they animated it, meaning they drew it frame by frame and more thought was put into it than drawing a character, a background, and then doing a cheap animation. I still wish they'd fix up the artstyle here though. If they could capture Kinu's art style from SFIII, put it into an anime form, that'd be great. Imagine that with a good storyline that everybody likes the direction of. Could be very cool.