My favourite Generation was Gen III. LeafGreen and Emerald were the two games that really got me into Pokemon, so that's probably a good part of why I like this Gen so much, but that's not all.
Gen III and an amazing world, Hoenn. It had many very interesting cities and locales, and was very fun to explore. The world was bursting with content, from the Contests to the Battle Frontier. It had many other fun feature such as all of the event locations and Secret Bases. I specifically enjoyed Secret Bases, as for me they added tons of re-playability to the game. I loved collecting rare furniture and designing my base.
In addition to the world, the Pokemon of Gen III were also quite good. Some of my favourite Pokemon come for Gen III, such as Keckleon, Tropias, and of course Mudkip. Gen III also had many legendaries to catch. Not only did it have Rayquaza, Groudon, and Kyogre, but it also had the three Regis, Latios and Latias, as well as event Pokemon such as Mew, Ho-Oh, Lugia, Jirachi, and Deoxys. You could even get a Johto starter by completing the Pokedex (in Emerald).
Gen III also introduced many of the exciting features that are now a staple of Pokemon. These include Contests, the Battle Frontier, gauntlet-style battle challenges and more enhanced multi-player. These are some of the reasons why Gen III is my favourite Generation.