What are they?

Pencil puzzles are basically stuff like Sudoku, Crossword, Kakuro, KenKen, and Nonogram. These puzzles are traditionally solved by gradually writing down the answer.

This page focusus on the puzzles that:

... are actually "pencil" puzzles (not riddles, physical puzzles, web-based puzzles, etc.)
... require logical reasoning (which excludes stuff like maze or word search)
... don't require cultural-specific or language-specifc knowledge (which means English or cryptic crosswords are out)

This doesn't mean I don't like the excluded puzzles though. Some other puzzles and puzzle-ish games I like are escape-the-room games, Notpron, the Layton series, the Ace Attorney series, Zach-like games, Return of the Obra Dinn, Baba is You, and Chants of Sennaar.

Where to find pencil puzzles

Many English-speaking puzzlers seem to gather at Grandmaster Puzzles.
The Cracking the Cryptic channel features puzzles (mostly sudoku variants, but occasionally other puzzle types).
There is the World Puzzle Federation which held annual championships (before COVID struck). There are also national championships such as Logic Masters India, US Puzzle Championship, Logic Masters Deutschland, and UK Puzzle Association.
Nikoli is a Japanese publisher specialized in pencil puzzles. You can buy physical magazines from them. (They used to have online puzzles but RIP.)
Toketa? is an annual magazine from Japan, featuring innovative puzzle types.
Janko.at (in German) has a large variety of puzzles.
If you don't mind machine-generated puzzles, Simon Tatham's Portable Puzzle Collection is available on the web and pretty much all platforms.
In my opinion, the best sudoku app is Sudoku & Variants by Logic Wiz (iOS, Android). It features tons of sudoku variants, extensive pencilmark entry modes, detailed hints, and weekly themed puzzles.
In my opinion, the best nonogram app is Nonograms Katana (iOS, Android). It features black-and-white and color nonograms up to 80x80, both from the creator and from other users. The control is very comprehensive and customizable.

Hybrid pencil puzzles

Some puzzles blend two or more types of puzzles together. These are more difficult to construct but also exponentially more fun to solve. Here are some of my favorites:

By Palmer Mebane (MellowMelon)
- Puzzle 200: Nikoli Octathlon
- Puzzle 300: Loop of Death
By Prasanna Seshadri
Friday Puzzle #100 - Another Milestone by Thomas Snyder
The Ludicrous Loop: over a thousand cells of circular logic! by TheGreatEscaper (William Hu)
Stupendous Sponge by boboquack
Super Sudoku by Cary Huang