1. KOF 2002: Unlimited Match
2. KOF XI
3. KOF 98
4. KOF 00
5. KOF XIV
HM: KOF XIII
Over the past few years I've decided to actually play though the entire series, to understand the backstory and game mechanics throughout the years. Before that I would just play KOF 97, and KOF 98 on arcade casually growing up. I appreciate all of the games and what they offered, but I had the most fun with these top five.
Played hours of '98 on Dreamcast (Dream Match 1999) and appreciate its solid gameplay engine. Although the character roster and combo engine just appeals to me more in '02 - especially Unlimited Match, IMO one of the best fighting games of all-time.
I've been playing '03 lately and while it added the tag mechanic it still felt unfinished and unrefined compared to XI smooth transitions from each character. Besides, having my favorite roster of characters with so many unlockable ones in XI, is my favorite tag-fighting game of all-time.
Similar experience playing '99, enjoyed the art-direction but in the inclusion of calling in your partner was too stiff. Was eventually re-worked in '00 iteration, including many bonus cameos for the fans. Truly one of my favorite of the series.
Despite owning XIII, I haven't invested as much times as I did with prior games of the series. Technically its one of the best fighters, but the overall excessive combos system would have the player focus on the same scenario rather than multiple options.
The latest installment of the series XIV did almost everything right (eventually improving the graphical department) huge roster, unique new characters, and solid gameplay drawing inspiration from earlier games of the series.