If you love detective stories then you should definitely read the Sherlock Holmes books. They're over a century old, but they're still very good today.

Tolkien's books (the Hobbit, and then the Lord of the Rings trilogy) are definitely the most famous fantasy and adventure books. Keep in mind that the Hobbit was written for children and the Lord of the Rings was written for adults, so the latter will be much harder to read (especially since Tolkien liked to play around with his words).

The Chronicles of Narnia series is another classic fantasy/adventure series.

I very recently read G.R.R Martin's the Song of Ice and Fire series. They're the books the show, Game of Thrones, (which is also the name of the first book) is based on.

Anything by Wilbur Smith is usually really good.

Thank you all, for your answers. To this momint I read many books from Isaac Asimov, and I realy like this author! I saw films in Russian: Hunger Games (first part), Hobbits, Lord of the Ring, Harry Poter (read first part in English version), Sherlock Holmes. But I realy like something new, bacuse first impression is important for me! You gave me new books and I will start read them, thank you very much! If anyone want to add his reading expirience - welcome!

As I understand, only Russians answer here:))))
offering a single genre:))) THen I'll be the furst russian boy to offer some American sci-fi in this thread

THen the same answer as everywhere: I read ton of sci-fi when i was a child  (the same that every Russian of my generation read).
THe only novel (but not the author!!!) I am able to single out was "City' by Clifford D. Simak.

I don't know, may be it is not that great as I thought when i was 10)))) But that's my only candidate for 'a favorite novel'

Part 2:

If the other suggestions are too difficult, here are a few aimed at younger audiences:
Deltora Quest - the language is VERY simple (I read the first novel, The Forests of Silence, in a single afternoon when I was six years old). Just make sure you the novel, NOT the comic book adaptation!

Eragon is another series with simple language. The plot is basically a mix of Star Wars and Lord of the Rings, and the first book was written when the author was 15. That tells you all you need to know :-D

The His Dark Materials series is pretty good.

Harry Potter... I'm sure you've heard of it.

I've mentioned the Hobbit already, but I'm mentioning it again here because the language really is much simpler than in Lord of the Rings.

I was a big fan of several books by Garth Nix as a kid.

That's everything I can think of for the genres you mentioned. If I think of anything else I'll let you know.