Today I saw someone who was in the 'Today's Birthdays' thing that didn't have an age next to his name. When I checked his profile it said '3 Oct 0', how is this possible?

That member's birthyear is not set, which is why it shows up as 0 in his profile. However, the confusing thing is that if you try to set yours as nothing, you get an error message of "Either complete all the birthdate fields, or leave them all blank - we cannot process partial birthdates". What's even more confusing is that I used to have mine as not set.

I think there was some sort of glitch or something that was changed awhile back, and members used to be able set their birthyear as nothing, but after that was fixed, you were not able to edit your profile again until you set an actual year (I remember getting that problem). Considering that user hasn't logged on since 2007, I think it's entirely possible that he set his birthyear as nothing during the time people were able to, and then hasn't updated his profile since then.

I could be wrong though, this is just my guess.

EDIT: Okay, I'm wrong. Ah well.

Does the lowest year you can fill in change every year? If so maybe he filled in 1909 last year and it changed to 0 this year...

Yup. I did this myself, and my birthday is listed as year 0 now.