Nob question indeed, but I never used Steam before and I'm clueless: I play Skyrim sometimes in online mode and sometimes in offline, and I don't know where to check what version my Skyrim is. Do I have to patch the game manually like I did with Oblivion, or it is ninja applying the patches without notifying me? Thanks.

you can tell by opening the skyrim folder, right click on the TESV.exe and select 'properties'. Then click on the version tab and it will show you what version of the game you have running.

While playing your game press escape. The version number appears in the lower left corner of the resulting screen. My game is presently 1.3.7.0. Yes, Steam updates all by itself.

Thanks you for the replies guys I just checked and I have 1.3.7.0