Key dates: I don't think there are any from the 1900's; from the 1800's, I'd say 1844, 1849 and 1863. The 1860 Young Head type is probably the "flagship" of the scarce farthings; the "Bun Head" type is much commoner. The 1895 Bun Head is also slightly scarcer than the 1895 Old Head.
Varieties: again, not much of interest from the 1900's, but there are plenty from the mid-1800's: the ones worth a premiujm are: I823 and I843 (I for 1 in date), 1851 tipped D, 1856 R/E (in VICTORIA), the 1860 toothed border/beaded border mule, and the 1874 H G/sideways G. There are lots of other varieties in other dates, too.
You should also be aware that from 1897 to 1918, farthings were intentionally blackened by the mint prior to being issued; this was to attempt to prevent confusing them with half-sovereigns, gold coins the same size as a farthing and with the same obverse.
Colonial: the only colonies I'm aware of that issued farthings were the Isle of Man, Jersey (where they were called "1/48th of a shilling") Guernsey (where they were called "2 doubles"), Ireland, and South Africa.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis