Dated 1 October 2011: There is no need to watch Shakugan no Shana II before watching the third season
I generally strongly discourage people from skipping seasons. Typically they do it so they can follow something shiny and new and/or watch something at the same time as their friends so they'll have something to talk about. This can lead to very poor decisions, such as watching Diebuster before watching Gunbuster, or watching Shikabane Hime: Kuro without watching Shikabane Hime: Aka. I have less of an issue with people skipping previous Mobile Suit Gundam seasons (at least for series in different continuities) since there are so damn many of them, or skipping previous Macross iterations, although I do insist on people watching the original Cho Jiku Yosai Macross; do not be tempted to lean on Do You Remember Love? instead. Good movie, but really not a substitute for the original series—not at all.
But while I feel it is wrong on principle to skip seasons, especially when one's reasons for doing so fall in the "shiny and new" camp, I can make an exception for Shakugan no Shana II. I watched 24 episodes of this second Shana season because I enjoyed the first season and wanted to give the upcoming third season a try. This may have been a mistake. Shana II is every bit as awful as its reputation warned me. Shana II is 24 episodes of tedium occasionally interrupted by insipid fights. It is WORSE THAN COSPRAYERS, I finished Shana II with great reluctance. It was never ever actually BAD in the way Limeiro CROSS or Macademi Wasshoi! were truly bad; it just wasn't ever compelling, or even interesting.
To put things into perspective, the multi-episode climactic battle at the end of Shana II kept giving me flashbacks to the Demonbane anime. Now, Demonbane is by no means good, but I have to say that it was at least more interesting than Shana II. This is especially true of the fights. I've long harped on J.C. Staff and its poor track record when it comes to animating fight scenes (excellent Azumanga Daioh snowball fight notwithstanding), but I remember even the worst Demonbane fights against the shrieking mad scientist to be more engaging than climactic season finale fight scene against the shrieking mad scientist of Shana II. And I'm not just saying that because Mr. Eroge Protagonist from the Demonbane anime had to soul kiss a book every time to make his giant robot go. Well, he didn't have to, probably. He just did. But I digress. Shakugan no Shana II is a horror, and I will be amazed if Shana III requires any foreknowledge of its preceeding season's events. Yeah, I'll still at least start Shakugan no Shana III. It's too late to turn back now. Who knows, maybe the odd-numbered seasons will be good.