Kirby, to tell you the truth (aka my opinion):
All the new or recently released games mentioned by others and myself in this thread are still overshadowed by the real classics of this genre. If you want to play games like Myst, Syberia and Atlantis, you can of course play their sequels, such as Myst IV: Revelation, Syberia II and Atlantis Evolution. If these games are still your favourites, I generally recommend you p&c games developed in the French speaking area (Benoit Sokal's Syberia is published by Microïds and Atlantis was originally from Cryo Interactive). Maybe other Microïds games would do it for you or the Penumbra series by Swedish developer Frictional games.
There are plenty of new releases each year and they are mostly unknown to anybody outside the group of die-hard p&c adventure fans. Everyone hopes to discover a new gem or a future classic, but (imo) the last game in this genre, which deserves the status of a classic today, was released in October 1998. The name was Grim Fandango.
The European games of then and now are nice to have, keep the genre alive and some of them are even good, but they simply can't compete with the US classics (only exception imo: 1990s Revolution Software's games from UK).
If you haven't played the 80s/90s adventures created by LucasArts, Sierra, Revolution Software, Westwood (or Dynamix), most of us would recommend you one or more of these classics - as you can see from the answers in this thread.
A friend of mine once asked me for a real classic in this genre, which is "graphically still playable today" (the gameplay is timeless anyway - either you like it or not), and I gave him the following LucasArts games:
Indiana Jones and the Fate of Atlantis, Day of the Tentacle, The Curse of Monkey Island, Grim Fandango, Sam & Max, Full Throttle
And these 6 are only on place 3 to 8 of my personal favourite adventure games (The Secret of Monkey Island and Monkey Island 2: LeChuck's Revenge are on top). IMHO LucasFilm/LucasArts was the best p&c adventure company ever (others may shout objection and name Sierra On-Line or even *cough* Brøderbund).
But to each their own. 
