I very much enjoyed the third generation. I got into Pokemon when the first generation games initially were released. However, I think I burnt myself out on Pokemon and the second generation didn't offer me enough to make it worth attempting. I skipped that generation entirely. When Ruby/Sapphire came out, I got back into Pokemon. Here's what I like about it:
- more Pokemon: Ruby/Sapphire introduced 135 new Pokemon. Since I personally had skipped second gen, that number was 235 for me. The Hoenn Pokemon were nice additions. I love the Torchic family, Skitty, Zigzagoon/Linoone, the Ralts family, and more.
- 2-2 battling: unfortunately this wasn't taken advantage of more completely until Emerald (even there I think more can be done) but I enjoyed this aspect. Old moves, such as Surf, could affect 2 Pokemon at once. Some of the stat upping moves gained even more usefulness. This added a whole new dimension to battling strategy.
- abilities: 99% of the time, I loved abilities in the game. I think the only time I didn't like them was when I ran into a Trapinch and didn't feel like battling but was forced to defeat it anyway. The abilities made some of the older Pokemon feel a bit more useful in battle, and some abilities made Pokemon useful to have in your party even if you weren't going to use them to battle. Zigzagoon/Linoone's Pickup ability got such useful items for me I had one in my party pretty much the entire game.
- breeding: I know this was introduced in second generation, but third generation's breeding felt more necessary and I liked that. You could breed Pokemon specifically to raise them up for contests or to try to get good IVs and natures. The combination of abilities and breeding (Pokemon Emerald) made breeding even easier as well.
- the first generation remakes: I know some people don't like these but I was happy to see Kanto come back. Kanto felt a lot more enjoyable with the 3rd generation additions of breeding, abilities, double battles, and more. I also liked that, thanks to them, we were able to get the rest of the Kanto Pokemon not available in Hoenn and a bunch of the Johto Pokemon.
- the Gamecube games: One thing that disappointed me about the Stadium games is that they didn't have a storyline. Colosseum and XD introduced a new region, a new Pokemon concept (Shadow Pokemon), and a new way to catch Pokemon (snagging). The fact that there weren't wild Pokemon to catch, the inability to walk from town to town yourself, and no gym leaders or Elite 4 disappointed some people but I still found them very enjoyable. Before Emerald came out, Colosseum was the only way to get the missing Johto Pokemon that were not in FireRed/LeafGreen and even now, the 2 games (plus their pre-order disc) are the only legit ways to get Jirachi, Lugia, and Ho-Oh without an event.
Unlike what happened after first generation, I don't feel burnt out. In fact, I'm more into Pokemon than ever before. I'm very much looking forward to seeing what fourth generation brings us.