Sudoku was fun, but the majority of the fun with any of these puzzles for me was figuring out solution methods for myself. Sudoku is now so heavily documented as to be trivial to solve, even at the highest difficulty levels (Especially if you have the patience to try Bowman's Bingo).
After getting burned out on Sudoku, I found out about Nikoli, and the other myriad puzzles they publish. At first I started with Hashiwokakero, then quickly moved on to Heyawake, Nurikabe, Hitori, Akari, Ripple Effect, Masyu, and even some not listed on the English version of Nikoli's website (Kin Kon Kan is particularly fun, once you figure out the rules).
In that time, I've ordered several books from Nikoli's website, traded for books with occasional Japanese acquaintances, and hunted Japanese auction sites for out of print editions. In short, it's expensive and time consuming to feed my language-independent logic puzzle habit. I'd be very happy if some stateside publisher would put out a magazine akin to Nikoli's "Puzzle Communication", or a compilation of new puzzles. I've seen a few books featuring other Nikoli puzzle types, but they do not feature more than 3 or 4 different puzzle types. Games magazine's puzzle magazines frequently feature Nurikabe and Slither Link, but only 2-5 puzzles per issue. What I want is variety and volume. Lots of different puzzles, lots of instances of each.
By the way, those with the ability/desire to import Japanese video games might want to check out Puzzle Series for the Nintendo DS. Volume 5 is Slither Link, Volume 6 is Illust Logic (Known to many as Picross, Nonograms, Edel, or Paint by Numbers), Volume 10 is Hitori, Volume 11 is Nurikabe, and Volume 12 is Akari (Light Up). You may also want to check out Simon Tatham's Portable Puzzle Collection. NetGame is particularly interesting.
And of course, no discussion of grid-based, wordless logic puzzles is complete without a mention of Solitaire Battleships, which currently cruises under the radar with the name Yubotu.