In Friends episode #78, "The One With Joey's New Girlfriend," Rachel's birthday is given as May 5th. This season's Christmas episode is episode #204. Episode #206 takes place on Rachel's birthday (May 5th) and makes reference to the events of episode #205 as being "yesterday" (May 4th). That would make it a just-over 4 month gap between episode #204 and #205. Just an observation. Rachel's birthday is also celebrated in episode #24, "The One Where Rachel Finds Out," episode #46, "The One With Two Parties," and episode #160, "The One Where They All Turn Thirty." I don't know if it's celebrated in any other episodes.

Wasn't it also celebrated in Jan. 16th's episode?

Yes, that was episode #206, "The One with Phoebe's Rats."