Do you know any good adventure games with actually logical puzzles? By logical I mean requiring more or less thinking and not a random clicking on everything. I used Google but did not find a lot (no or almost none adventure games that are not about random clicking?).

Games I played and seem fine in this regard:
Broken Sword (not really used walk-through, although I did not finished it so maybe later its worse, but I doubt it)
Sanitarium (walk-through used once for missed item)
Beneath A Steel Sky (use walk-through a couple of times. but still puzzles make sense overall)

So overall Sanitarium is good example of great logical game. I would like to now about more games like that one.

I heard that The Book of Unwritten Tales is also very good and has normal puzzles.

Couple of example games I have played:
Monkey Islands - I like them, but puzzles are mostly retarded,
Day of the Tentacle - did not like it - puzzles are stupid as hell and totally illogical
Grim Fandango - puzzles seemed strange and not so logical
Gabriel Knight: Sins of the Fathers - I was stuck but the puzzles did not seem retarded
Space Quest 1&2 remakes - I really liked games, but played with walk-through (it's hard without and tedious)

The Myst series. It's almost pure puzzling.
The Room is pretty good too, although I don't think it really counts as an adventure game since there's no real story to speak of.
Oh, and how could I forget the masterful Sherlock Holmes games from Frogwares?
Your problem there is you listed a lot of humor games. Those tend to have some pretty wacky logic for the sake of being funny, especially from LucasArts.

I actually played a demo version of some Myst like game in the 1990's and I enjoyed it. Still the problem I have with Myst games is that, as far as I know there is no characters in there. No dialogs really. Only puzzles. I would rather have something like Sanitarium - story, characters, and puzzles.

Sherlock Holmes might be interesting.

I did not need a walkthrough for Fran Bow, so that means that I guess. And confirmation on Book Of Unwritten Tales.

Companions of Xanth - just remember to use Xanthian logic: EVERYTHING is a pun ;)

Still Life has got several really good puzzles and an engaging story plus rich atmosphere to boot.

If you consider it an adventure game: The 7th Guest is made mostly of puzzles. Just like its sequel The 11th Hour. It has a solid story: I loved it, but it has no adventure-cum-RPG elements like dialogue or inventory management; the story is told by solving puzzles and interacting with the environment.

Star Trek: 25th Anniversary, and Judgment Rites. Mind, you do use the various Tricorders and personnel to shed light on things, which can give you a good idea of what to do - or not. Failing a puzzle doesn't automatically stop the game, and is instead likely to result in a Red Shirt meeting his fate in short order. Only after such a grievous mistake would the main cast lose their plot armor.

I could recommend similar Myst-type games like Schizm or Rhem, but I don't think any of them can really be found these days outside of a physical copy.
You might like Return to Mysterious Island, Voyage, or SafeCracker.

The Longest Journey is excellent in that regard.

It happens to be the awesomest adventure game to grace us lowly humans to boot (because I say so).

I rarely play adventure game. But Syberia is pretty logical

Pretty much any of Wadjet Eye's games. I don't remember ever having to ask/look for help for any of these as logical thinking within the boundaries of the game got me through. It may have taken me a while in certain places, but none required freak brain acrobatics.
As much as I love that game, there are a number of puzzles in it that feel quite convoluted.

I'm generally not a fan of this genre but I really liked Machinarium. It has a beautiful hand-drawn art style, a wonderful soundtrack, and most of all it has really good puzzles. I almost never got lost and if you get really stuck you can play this little 'shmup minigame to get the puzzle solution if you feel like looking up the answer is cheating. There is one slider puzzle but its far from the worst offender when it comes to the slider puzzles I've done. It also doesn't really have dialogue (Like the other games by Animata Design) and instead tried to convey information through character movement and pictures which is unusual for a genre that's usually really heavy on the dialogue. Its one of my favorites and I'd say its worth a shot.

As one can tell by my avatar, I quite enjoyed Gemini Rue. No moon logic there. Which for me, who is terrible at most adventure games despite liking them, was pretty great.

Although I believe more seasoned adventure game fans found it a bit too easy. I will admit there was more than one "Use Gun on X" puzzle in the game, but that's what being logical gets you.