In Gen I you had three legendaries, Articuno, Zapdos, and Moltres, and Articuno was the only to easily miss if I recall. There was also a final boss legendary, Mewtwo, and one event-only(unless you glitch or hack) Pokemon, Mew. Gen II had two legendaries that the game pretty much tells you when they are available, and even tells you where Ho-oh is(Lugia is a bit harder to find), plus three other legendaries you have to randomly encounter, plus one event-only, Celebi.
Gen III has no less than eight legendaries(not counting event-only Pokemon), 5 of whom are version specific - Groudon for Ruby, Kyogre for Sapphire, all three for Emerald, and whichever Lati_s was red for Ruby, the blue one for Sapphire, and Emerald gives you the option of which one you want to encounter(the other becomes event-only after you grab the first one). Lati_s also teleports around every single battle or area change. The other three require doing this ridiculous puzzle that I haven't figured out yet even with a guide that involves being able to read Braille and first getting two fairly hard to get Pokemon(Relacanth and Wailord), any other 'mon with Dig(there is exactly one TM in the game, as far as I know), and doing some other stuff. There is also at least two event-only Pokemon, Jirachi and Deoxys, not counting legendaries from the previous game.
Gen III also has a non-legendary that deserves mention, Feebas and its evolution, Milontic. Feebas can only be fished up on Route 119(by the Weather Institute). It can only be found in one of six(and only one of those six) water tiles, the positions of these six tiles determined by from what I can tell are a combination of the Dewford trendy saying and your Trainer number, and there's no guarantee that you'll even get Feebas on the first try. Evolving it is even more ridiculous, as the first thing is that Feebas you worked so hard to get also must have one of only four of all the possible natures, the four that focus on the Beauty trait. Then you must feed the butt-ugly fish enough candy to make it so beautiful that the Fanclub Chairman gives you the Blue Scarf if you didn't already get it. I don't even know what the next step is, the guide didn't say, but I think it's either trade or level-up.
For clarity, event-only means that you have to bring your GBA to a Nintendo game event, which are all long over, so you need to hack the game to get them now.