TEKKEN 3 / Namco / Arcade
It doesn't play all that different from either of its two predecessors, but for some reason Tekken 3 was the first of the series I really enjoyed and wanted to spend a lot of time with.
I guess the first major factor is that the CPU isn't stupid hard at all settings like it was in the prequel, allowing you to actually have some space to experiment and learn the different characters. Tekken 3 is also a pretty significant graphical step forward from the first two games, a result of Namco moving to a new generation of arcade boards.
There are a lot more characters, and a greater variety of fighting styles too. The old characters largely keep their familiar movesets, but with about twice the development time as that between Tekken and Tekken 2, the game has had significantly more tweaking and feels a lot more balanced than the previous two.
Overall changes to the fighting engine also make a significant impact. This was the first game in the series to allow you to sidestep up and down a la Virtua Fighter 2. While low-level and casual play doesn't see much benefit from this, since the steps are small and execute kind of slow and don't usually move out of the range of a lot of sweeping moves, apparently it added a new dimension to high-level play. I'm a "casual" player myself and what I appreciated was the shorter, tighter range of jumping, as well as the addition of more mid-range and low-range moves, expanding the scope of combat beyond sort of robotically standing around trading and blocking your best high-hitting combos until someone fucks up or gets in range for a throw. It's also possible to do quick recoveries from the ground, making life harder for those cheeseball asshats that like to Rape Ape all over you once you're knocked down.
The arcade version is still all about competitive play, though, with the same scanty endings as usual and not much going on beyond the typical gauntlet of 8 battles always ending off with the same bosses. If you're interested in this one but going to be going solo a lot, check out the port for Playstation, which adds a bunch of bonus modes at only the price of a small graphical downgrade.
* Gameplay Video