Well, for starters - what Pokemon game are you planing to play?
At any rate though, I shall throw various links at you. First off, each handheld game gives you a choice of one between three starter Pokemon. So if you want each of those, you'd have to restart the game 3 times and trade each one to another game before doing so, or trade with other people. (This is less of an issue if you have the 4th gen games and Wi-Fi).
As for game-specific legendaries/one-offs:
https://www.serebii.net/pokemon_advance/legends.shtml - Legendaries in Ruby and Sapphire.
https://www.serebii.net/emerald/oneoff.shtml - Emerald. Note that a fair few double up from R/S, and some of these are Event-only Pokemon (require a 'ticket' item), which have stopped long ago.
https://www.serebii.net/red_green/legendary.shtml - Fire Red/Leaf Green
As for the 3rd-gen Gamecube games - Colosseum has the three 'Johto' starters (all of them - one during the main storyline, and the other two from side quests following the main storyline - you get lead to them, basically), and the Johto legendary beasts (Suicune/Raikou/Entei) - during the main storyline and unlimited chances (albeit they're very hard to get outside of these games). Also, Ho-oh, which is only obtainable from beating Colosseum, purifying each Shadow Pokemon, and then taking on Mt Battle (a 100 trainer challenge) with a registered team from start to finish after you do so. Upon defeating that you get Ho-oh.
And XD: Gale of Darkness has the Kanto legendary birds, and Lugia - again, unlimited chances for these.
As for 4th gen games - Diamond and Pearl:
https://www.serebii.net/diamondpearl/legendaries.shtml
Platinum:
https://www.serebii.net/platinum/legends.shtml
One other to mention is Feebas (and it's evolution) - a notable rare Pokemon that is hard to find without knowing how to.
https://www.serebii.net/games/feebas.shtml
That should do for starters. Others are ones that evolve only by trading, or evolving with a set move, and so forth. There's serebii.net's dex for that, I suppose, and also bulbapedia as mentioned by Flex_S.
Hope that helps.