The answers below are well thought out and mostly correct; however, I have been contemplating this same feat myself and have found 4 more "unobtainables" / legendaries that can be gotten that are listed as "event exclusive". They are as follows:
#1. Jirachi
For this you will need a Gamecube, the bonus disc that came with Pokemon Colosseum and a GBA Link Cable (can be found on eBay for ~$5) and one of your third gen games. The bonus disc can be used to upload one copy of Jirachi to each cartridge from that era (Ruby, Sapphire and Emerald)
#2. Phione
For this you will need a Wii, the WiiWare game My Pokemon Ranch and either Diamond or Pearl. Hailey will offer trade you one once 350 Pokemon are in the ranch (they don't have to be different and they don't have to all be from you either, she gives you one each day just for playing, sometimes more). Or you could breed the one from #3...
#3. Manaphy
For this you will need two DS's, Pokemon Ranger and Pokemon Diamond or Pearl. Beat missions in Ranger to unlock Ranger Net, under that hold R, X and left to access a password menu. Enter the appropriate password dependent upon your game's region and "check egg" will now replace the Ranger Net button, turn on the second DS with Diamond or Pearl loaded and get to the menu screen (continue, new game) and select check egg on the first DS. Your Manaphy egg will now be transfered into Diamond/Pearl!
#4. Mew
My whole reason for this quest in the first place. They said it could only be gotten in first gen games, but they were wrong! Following the same procedure as #2, keep importing until you have 1000 Pokemon in the Ranch, Hailey will say that she would like to recapture her love for Pokemon as she knew it when she first starting collecting or something equally as poetic and offer to trade you a fully legitimate Mew for any Pokemon egg.
Honorable Mention: Celebi
Celebi was given away by having used the Pokemon Bank service between February and September of 2014 as a gift.
There you have it, one step closer to "catching them all" ;)