Best:
1. Grand Theft Auto III
When it came out, there was really nothing else like it. Now, good sandbox games are a dime a dozen--Assassin's Creed, Just Cause, Saint's Row, inFamous--but at the time, you could play GTAIII for hours on end and just bask in the then-revelatory shedding of level structures, and how interdependent its whole ecosystem was.
2. Sid Meier's Pirates!
Civilization is brilliant, yes, but one thing Pirates! has on it is that its single-player occurs in a continuum--rather than being forced to discard your civilization and start over, the forty or so hours it takes to complete Pirates! are never interrupted. Better than StarCraft, Red Alert, etc., and an unadulterate masterpiece of design, this kick-started the heyday of PC design in 1987 along with Maniac Mansion.
3. Shenmue II
It never sold much, but it was definitely influential--the QTEs, infamously, but the ambience of its storyline, and its pacing, can be detected in everything from Heavy Rain to Red Dead Redemption. What really set Shenmue apart was how its gameplay was structured around the story rather than the other way around, yet rarely seemed slapdash: the Virtua Fighter engine supported it in ways the sole use of QTEs in Heavy Rain never could, and wandering around neon-lit Hong Kong at night only to find your journey had to be interjected with a dayjob the next day so you could afford a hotel to stay in carried the definite accent of reality; of the consummation of narrative in video games.
4. Deus Ex
The last word in FPS design occurred just one year prior to Halo: Combat Evolved, which ushered in the era of shooters dumbed-down for console, including--regrettably--DE's own sequel. Part of what's amazing about DE is how much is done with so little: you had this ragtag Unreal engine, but the plotting was so excellent, the ways you could approach each scenario so fascinatingly varied, and the levels so well-designed, that it achieved a level of immersion basically unparalleled in modern shooters. Moreover, it's ethical choices avoided that common binary--DE wasn't just good vs. evil; rather, it recognized the inherent subjectivity in morality by never making the consequences of choices explicit, and thusly forcing the player to apply their own sensibilities. It's amazing to think that it only took seven years for FPSes to get to this point after DOOM, and that the next seven concluded with BioShock, which was basically just a simplified, claustrophobic version of DE with better art design.
Worst:
Metal Gear Solid 4
Only a game in the nominal sense; what gameplay there is is uninteresting.
Final Fantasy X
Once again, an offender for having too much FMV, but even the gameplay leftover was mostly uninspired, point A to point B stuff, and the implementation of voice acting actually hurt the credibility of the narrative. A huge disappointment after FFVII and FFIX, and--as the first FF Hironobu Sakaguchi didn't contribute to in any meaningful way--the beginning of the decline of the series.
Red Faction II
In which Volition tries to make a "serious" shooter by reducing the use of Geo-Mod in favour of linear missions and reducing the length of single-player in favour of multi-player content and ends up eliminating any reason you had to play Red Faction in the first place.
No More Heroes 2: Desperate Struggle
Not so much a bad game as a disappointment, No More Heroes 2 lazily declined to make any of the improvements you'd expect of the original--creating a more populated world map, diversifying gameplay, etc.--instead opting to just eliminate the world map altogether and offer eight new boss fights modeled exactly after the template of the first game (oh--and he added lengthier cutscenes, which are always the scourge of improved gameplay). For a guy whose mantra is "Punk's Not Dead", this is some pretty tepid shit.
Castlevania: Curse of Darkness
For those who thought the Library in Halo was bad, take heart--every level in this game is the exact same maze, just populated with different tilesets. Honestly, it's as if the developers conceived of a really neat weapon customization mechanic, then just figured that would suffice and cut and pasted the entirety of the game out of art assets designed for the first level; a decision analogous to making every level in GoldenEye some rejiggered varation of the Basement and rationalizing it because there's a large arsenal of weapons. Which is especially a shame, since--beyond the cool weapon-designing--this actually has some great boss fights.