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I can't pick a single favorite, but my favorite series is definitely The Age of Infinity (I do looove Phoenix Wright, but that has too much gameplay to be a strict VN, and as long as I have a hard time choosing a favorite, I'm using that to put Age of Infinity ahead, hurr).

I guess I'll go with Ever17 as my recommendation for the series, though Remember11 was really good too (despite some serious drawbacks ;_; ). Ever17 had one of the best plots I've ever seen in any medium EVER, and used every weapon it had as a visual novel, even on levels I would never even have thought of. There are no glaring plot holes, the art is nice, the music is excellent, and it's just an AMAZING game. It's never a chore to see all the endings, either, since you can save a bajillion times and skip all dialogue you've already read. The True Ending is mind-blowing.

It's like $200.00 for an actual copy these days (PC in English), but I give to you a download link!

(Link removed due to TOS violation >_> )

Also, 999: Nine Hours, Nine Persons, Nine Doors is a fantastic game as well, by one of the writers of Ever17. It's for DS and is getting hard to find in stores, but I'm pretty sure you can still get a copy from the publisher.

999: Nine Hours, Nine Persons, Nine Doors

It's about a group of nine people who find themselves kidnapped onto a sinking ship with a numbered watch on their wrists, a bomb in their stomachs, ominously numbered doors, and both a strict set of rules and a time limit to band together and find "the door bearing a 9". The game is very dark and features descriptions of gore, but is extremely satisfying, story-wise (except for one thing, warning you ahead of time, in case you're one of those VN-players who has to have EVERYTHING tied up and can't forgive things like that), and presents some very thought-provoking concepts. There's puzzle-solving gameplay, which is very solid as well, most of it numbers-based (unsurprisingly). You only get one save file, but you can skip all already-read dialogue in your bid to get the True Ending (and believe me, you will want to).

My favorite VN is called KiraKira. It's made by Overdrive, and is available in English from MangaGamer, in both an All-Ages and Adult version (I played the all-ages version). It's a school rock-comedy about the second literature club at Ohbi academy deciding to do something really special for their final school festival. Not only are they seniors, but the club will be shut down the next year due to lack of interest. They decide to start a band even though they know little about music, but they are soon pulled into the exciting world of indie bands, live shows, and the love of music. I've never played an instrument myself, but I love this game because it has great characters and romance, and everything about the story seems pretty accurate musically (the guy in charge of Overdrive plays in a band himself). I recommend everyone to at least play the free demo just for fun. You can also purchase the game here:
KiraKira

The adult version of the game can be found on the 18+ section on MangaGamer's website. It contains only about 7 adult scenes (and this is a very long game), so the all-ages version doesn't really feel "watered down" or anything.