Point-and-click (adventure) games

Sam and Max series (hysterical!), Ben There, Dan That!/Time Gentlemen, Please! (excellent dialogue and brilliant fourth-wall breaking) are ones I've played. Also played a bit of Gemini Rue, and the story's shaping up to be pretty neat. I haven't gotten around to playing Machinarium, Botanicula, Resonance, Hamlet, or The Dream Machine, but heard they're all really good. REALLY wanting to try the Strong Bad game, too.

The Longest Journey, Sam & Max, Runaway series, A Vampyre Story

There are a lot of decent point-and-click games, especially if you're willing to look into the "origin" aka, older point-and-click games.

LucasArts (Indiana Jones, Monkey Island), Sierra (Police Quest, King's Quest, Space Quest, Quest for Glory, Conquests of Camelot, Gabriel Knight, Phantasmagoria, Laura Bow) are the two of the best known publishers/developers from those times, I think

Some I enjoyed: Dragonsphere, Lure of the Temptress (both kinda short), Call of Cthulhu: Shadow of the Comet (Prisoner of Ice is also a decent game from Infogrames, though I never finished it), Flight of the Amazon Queen, The Legend of Kyrandia trilogy, etc.

I would really suggest I Have No Mouth, and I Must Scream. A solid and perhaps more complex story than your average point-and-click game. Certainly more mature, in which your actions have consequences.

For a more recent publisher, I would go for Daedalic. I love the intro music of The Whispered World ^^
I have not finished Dead Mountaineer's Hotel yet, but it seems okay. Even though the voice acting is dodgy (the protagonist seems really bipolar, sounding irritated and angry for no reason sometimes..which is odd and slightly amusing).

So many classic adventure games listed already but I'm a little disappointed that Full Throttle got missed out, although the Monkey Island series is probably my favourite.

Serious Sam. I mean, you point at monsters, click the mouse and watch muthufuckas explode, that's what they call point-and-click, right?

The walking dead and other telltale games like monkey island and back to the future.
Broken sword series, especially 1&2.
Runaway series are really great too and other pendulo studios games like yesterday and the next big thing.

Monkey Island series, Longest Journey series, Myst series, Sam & Max series

These are a good start ;-)

edit: I forgot the best: Broken Sword series!!!

Syberia

Nice thread, I'm gonna add some to my game wishlist :)

Maniac Mansion: Day of the Tentacle

Sam and Max: Hit the Road

Sam and Max: Hit the Road
The walking dead
maybe broken sword

A Vampyre Story,Agatha Christie: And Then There Were None,Agatha Christie: Murder on the Orient Express,Agatha Christie: Evil,Under the Sun,Amerzone,Atlantis: The Lost Tales (Rerelease),Atlantis II: Beyond Atlantis (Rerelease),Atlantis III: The New World (Rerelease),Atlantis IV: Evolution,Atlantis V: The Sacred Legacy,Aura: Fate of the Ages,The Black Mirror,Broken Sword: The Sleeping Dragon,The Cameron Files: Secret at Loch Ness,The Cameron Files: The Pharaoh's Curse,The Crystal Key,Cypher / Traitors Gate 2,Dark Fall,Dark Fall: Lights Out,Dead Reefs,Dracula: Origin,ECHO: Secrets of the Lost Cavern,Evidence: The Last Ritual,The Experiment,The Hardy Boys: The Hidden Theft,Keepsake,Crime Stories,The Messenger,Missing: Since January,Mysterious Journey II,The Moment of Silence,Next Life,Nibiru: Age of Secrets,Outcry,Post Mortem,Return to Mysterious Island,ROTS-1 Riddle of the Sphinx,ROTS-2 The Omega Stone,Sam & Max Season One,Safecracker: The Ultimate Puzzle Adventure,Schizm: Mysterious Journey,Realms of Illusion,Secret Files: Tunguska,Secret Files 2: Puritas Cordis,Still Life,Syberia,Treasure Island,Voyage: Inspired by Jules Verne,Sherlock Holmes Franchise.

Search for Dreamcatcher aka The Adventure Company.

The Walking Dead And The Hector Series! =D

That would be The Longest Journey, Dreamfall (The longest journey sequel), Deponia, Discworld (you can play it using dosbox or scummVM), Książe i Tchórz (hmm translation would be Prince and Coward), Jack Orlando, Gemini Rue, Blackwell and more

Machinarium.

Blade Runner :)
A bit oldish (1997) but excellent.
Not even GOG has it...

Nobody mention White Chamber? Maybe it's short but I'm sure that it's interesting and free.

I'm actually quite enjoying Ben There, Dan That, the dialogue is excellent!

Syberia.

The Secret of Monkey Island

my favorite so far has been gemini rue

Jolly Rover!

I guess people have been recommending these already but I'll just +1 the Daedelic games (Deponia, Chaos on Deponia and so forth) and all games from LucasArts. You can't go wrong. :)