Here were some of the milestones reached by games this generation:
Sonic Adventure - On Dreamcast in 1998, the first showing of robust worlds, sharp textures, and flashy effects of the generation.
Soul Calibur - On Dreamcast in 1999, a leap forward for fluid control and perfectly-matched smooth animation, bolstered by dramatic lighting in classically beautiful settings.
Dead or Alive 2 - On DC-arcade in 1999, a high-detail display (with 3,000,000 polys per sec, 2 infinite lights, 2 point lights) of large multi-tiered stages and seamless level progression (no loading pause) as well as tag-team matches with more than two simultaneously on-screen fighters. Reactive, real-time inverse kinematics and class C2 interpolation for fighters convincingly allowing them to take location-based damage on their bodies as well as crumpling well against walls, over undulating terrain. Nice animation touches on face and hand morphings as well as multi jointed and meshed movement on clothing and accessories. Cinematic usage of motion blur and cross dissolve.
Crazy Taxi - On DC-arcade in 1999, a large-scale world modeled in 3D, replete with liveliness from a working traffic system where high volumes of vehicles stop at intersections, use turn signals, pass each other, etc and whose status is tracked for a radius of a few blocks. A step forward for vehicle and object physics with cars capable of outrageous stunts and obstacles like stacks of boxes able to be sent scattering in various directions, all within an exceptionally solid engine providing for a fast and smooth ride.
Shenmue - On Dreamcast in 1999, the realization of focused detail in a large-scale world - hundreds of rooms and characters all distinct from one another; individual behavior and context for each NPC; dynamic weather and passage of time; real-time lip-synching; all dialogue spoken; complete status tracking of characters throughout the full world (a character delayed or redirected along their daily routine will adjust and stay that way, even when you’ve left the area and loaded in a new one); seamless loading of characters and their animation for daily routines; sound mixing of more than one chip-generated song at a time and lots of ambient channels; and countless animation subtleties where cooks kneed their dough, cut their vegetables, wash their pots and shopkeepers stretch their backs or beckon to window-shopping passerbys.
Seaman - On Dreamcast in 2000, combining quality voice recognition into a psycho-analyzing virtual pet, simulating entertaining conversation.
Virtua Tennis - On Dreamcast in 2000, the advancement to a truly responsive control and fluid animation mechanic in the compelling back-and-forth of tennis. A photorealistic court display of textures, lighting, convincingly-moving characters and encroaching shadows, and top-notch ball and object (in the mini-games) physics.
Jet Set Radio - On Dreamcast in 2000, the most wholly original and groundbreaking work of the generation, from intuitive play mechanics which turn urban locales into stunt parks, from its graphics which kicked off an industry cel-shading revolution and present an innovative hand-drawn look with 3D dimensionality in special effects like smoke clouds and explosions and in lighting and cinematic speed effects, from its highly stylized larger-than-life urban-anime themes, and even to its unique brand of techno, house, and party music. Complex environments and seamless loading through levels.
(Virtua Fighter 4) - On Naomi 2 (which I suppose means it doesn’t exactly belong on a console list for the generation) in 2000, extremely technical yet accessible fighter pushing advanced models, lighting, and character and object animation.
Phantasy Star Online - On Dreamcast in 2001, the establishment of a networked action RPG on consoles with expected user-friendliness, connecting players on a worldwide scale together for adventuring effectively with the use of a universal translator. Unobtrusive interface for fast communication of commands and emotions as well as more complex sentences across language barriers.
Sonic Adventure 2 - On Dreamcast in 2001, a showcase for smooth speed, image and texture clarity, and lighting touches.
Gran Turismo 3 - On PS2 in 2001, modeling with artistic and technical excellence, and nice cinematic touches.
Metal Gear Solid 2 - On PS2 in 2001, polished cinematics and animation with well-modeled physics interactions.
Guilty Gear X - On Dreamcast in 2001, hand-drawn 2D finally looking as vivid as a page out of a comic book on screen, with its high resolution (though, movement and animation not quite as tight as Capcom’s.) Perfectly smooth through native proscan and VGA from DC, and later sequels on DC-based Naomi and Atomiswave are looking prettier in each new iteration.
Rez - On Dreamcast in 2001, the synergy of reactive music, visuals, and force-feedback with the rhythm of the play challenge. Imaginative and abstract aesthetic and thematic design, creatively using overlooked approaches like vectors and wireframe shapes.
Halo - On Xbox in 2001, the achievement of a feeling of free will within a living epic battle, where allies and enemies react with convincingly unscripted independence and the physics fortunately don’t leave lots of elements and possibilities out of play. A step forward for optimized usage of full surround sound.
Rouge Squadron II: Rogue Leader 2001 - On GameCube in 2001, expansive, richly detailed worlds with lots of objects and action.
Baldur's Gate Dark Alliance - On PS2 in 2001, sharp display with supersampling and well-rounded environments and effects.
Jet Set Radio Future - On Xbox in 2002, pulling off highly detailed worlds with levels of great complexity and the allowance for seeing all the way across them from up high, cinematic special effects, and smooth speed all together.
Wreckless - On Xbox in 2002, a barrage of cinematic effects and filters, with photorealistic embellishments and lighting.
Grand Theft Auto 3 - On PS2 in 2002, large-scale world seamlessly running tons of interactions and well-crafted logic to allow for emergent play possibilities.
The Elder Scrolls 3: Morrowind - On PC/Xbox in 2002, the largest amount of content and interactivity ever spread across a massive game world, allowing for emergent progression.
Splinter Cell - On Xbox in 2002, solid mixture of shadowing schemes as well as nice physics modeling of object behaviors.
Panzer Dragoon Orta - On Xbox in 2003, graphics with CG-level robustness in modeling and multi-texturing, all framed with cinema-grade effects and showered with particle madness. Inspired artistic direction fleshing out an entire alien world of exotic plants, creatures, civilizations, architectures, and landscapes, where even the behavior and movements of totally original biomech creations are believable in mannerism compared with actual animal-like organisms. An otherworldly story with a very unassuming beauty and human touch to it, made all the more powerful from its honest delivery and lack of typical contrivances for the audience.
Dead or Alive Xtreme Beach Volleyball - On Xbox in 2003, strong modeling and high detail almost reaching a look of interactive CG within restricted environments.
F-Zero - On GameCube in 2003, impossibly smooth yet equally controllable sense of speed, rocketing through flashy roller-coaster courses.
Outrun 2 - On Xbox-arcade in 2003, draw distance and detail taken to another level, and smooth modeling of the car’s suspension as it drives with slick animation over the roads and hills.
Ninja Gaiden - On Xbox in 2004, the expansive world of an action game at the detail level expected only of a fighter with their more-forgiving requirements.