Question

I know you can get the 3 legendary birds, mewtwo and 1 of the 3 legendary dogs (depending on your starter) but are there any other very rare or legendary Pokemon in Fire red?

Answer 1

Those are the only legendaries you can get without an event or trading.

Lugia, Ho-oh, and Deoxys are available on Rainbow Islands 8 and 9. However you needed to attend a Nintendo Event to get the pass to go to these 2 islands, and the event has passed.

http://www.serebii.net/red_green/legendary.shtml For more information.

Answer 2

Http://serebii.net/red_green/legendary.shtml

Those are all the legendaries obtainable in Pokemon FireRed/LeafGreen. The other Pokemon require events to obtain.