Or never?

I already joined the Stormcloaks, but I haven't returned Ulfric's axe back to him, so I haven't started the Battle for Whiterun or anything.

I'm only asking because I don't want to go through Season Unending and risk screwing up the negotiations and dealing with all the confusing Jarl replacements, making it more difficult to become Thane .

But I also don't want to complete the Civil War quest and basically destroy Whiterun and Solitude, which makes one of Vex's guild quests impossible, and just looks really unpleasant in general (Seriously, that little market place around the well in Solitude and the nice area around the Gildergreen tree were some of my favorite spots - all ruined)

At which point do you guys usually complete the Civil War questline, if ever?

If you're wanting to do the main quest and the war, I recommend doing the main quest first.
Season Unending is probably the best quest in the game.

I usually do the main quest first, simply because calling Odahviing to clear out enemy forces at Whiterun and any forts is highly entertaining.

Unless My character is made for getting the Civil War done ASAP, I tend to save the Civil War until long after the Main Quest.

The way most of my characters and myself see it, the threat of the Dragons is more important that the pissing match between Ulfric and Tullius, and the prefered order of main quests for me is Skyrim --> Dawnguard --> Dragonborn (In order of threat level to Skyrim). I am more concerned with helping the everyday people of Skyrim than joining in a war that, regardless of what side is followed to completion, has no real victors. With all this being said, if any of my characters decide to do the Civil War questline, they do it dead last.

Definately NEVER!!!

I've only done it once, and that was more to be able to kill Ulfric Stormcloak, than to have the other side win. My character just couldn't let Ulfric live!

I did both quests at the same time, when it made sense to anyway. It worked out fine.