As the title says, very often Skyrim just shuts down. No error or anything. And then Steam starts updating it. I have no idea what kind of update and it's not very big, perhaps a few MB. And since it's happening more and more frequently, it's getting kind of annoying. Does anyone know what it is?

I suspect these two things are actually unrelated. Cloud Sync is enabled for Skyrim by default now, which means that whenever you close out of Skyrim (or it CTDs), it will upload your saves to Steam's cloud storage. That's the "update" you're seeing every time the game closes out--it's actually your most recent saves being synced to the cloud.

If you disable Steam Cloud for Skyrim (right click on Skyrim in Steam -> Properties -> Update tab -> uncheck the "Enable Steam Cloud synchronization..." box), do these "updates" persist? I suspect they won't. (I recommend disabling Cloud for Skyrim in any event, since I'm not sure what effect cloud syncing will have on people who play mod roulette with their load orders, and it takes forever to sync Skyrim's large saves anyway.)

As for why Skyrim is crashing...that mysterious close out without an APPCRASH log is typical of Skyrim. For some reason error reporting isn't enabled. I haven't had a CTD (outside of the game crashing when I exit to main menu from in-game; that was introduced in 1.5) in Skyrim in ages, however. Are you running any mods? Ini tweaks? One of those, or a few of those not playing nicely together, are likely the cause of your CTDs. I've seen a lot of reports of instability with certain mods, or certain mods combining their powers to turn Skyrim into Russian Roulette.

Steam will only download updates* when it thinks you're "idle"--in other words, not in a game. Any game. Steam will always wait until you are online but not in-game to download game updates for you. It will never close a game just to update it; it will wait until you quit. (Or it crashes.)

* One exception for this I've found is Dota 2. For whatever reason Dota 2 will always download its updates no matter what I'm doing, even when I'm in game. It's the only title in my Steam library that does that however.

The update is not an update, it is syncing. It saves your saves to steam cloud.

As for the CTD, idk.

I beleive this is recently happened to my attempt to play. Verified cache and defraged files, but Steam will not allow game play at all until 1 item down load finishes. At 156kbs and 2 hrs 40 min estimate before its ready to be used again, this is not going to work for me.