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