Mew is obtainable in a myriad of ways, but you can also get one in My Pokemon Ranch by transferring 999 Pokemon to the ranch. Since the Wii Shop Channel will be closing soon and there isn't a way to add Wii Points to your account, this method is pretty much inaccessible unless you already bought the game or you happen to have 1000 Wii Points.
You can get Jirachi with the Pokemon Colosseum Bonus Disc, or from Pokemon Channel in European countries. The Japanese version of the bonus disc instead gifted a Celebi.
You can get a Manaphy egg in Pokemon Ranger: Shadows of Almia, provided the gift hasn't been redeemed yet.
On that note, you can also get Manaphy, Deoxys, Darkrai and Shaymin from Guardian Signs, but sadly, these events have all long passed and are pretty much inaccessible now without the use of a cheating device.
There was a Celebi event from Pokemon Bank, but it ended a long time ago to my knowledge.
TL:DR: Nowadays, most events are done via wi-fi services and I think those are your best shot at obtaining Mythical Pokemon.
Let me know if I missed anything. Thanks!