A prefix of many hats, ur- has the potential to confuse the unwary reader. But as a rule of thumb, when in doubt, it means pee.
Along with uro-, ur- refers to urine, the urinary tract, or urea. Found in word like uretic, uric, and diuretic.
From Latin, but originating in the Greek our- or ouro-, from ouron, meaning urine.
Along with uro-, ur- also refers to a tail. From this meaning we get words like uropygium, urochord, and uropod.
Also from Latin, again stolen from Greek: our- or ouro-, from oura, meaning tail.
Ur- is also a prefix meaning original, primitive, or prototypical. The 'original version of' something. This is oft used today to create new words; Ur-feminist, Ur-grue, Ur-element, Ur-Hamlet. It may be hyphenated or separated from the word it is referring to by a space. It is often capitalized as a proper noun.
From the Greek ir- or ur-, meaning abide. It comes to us by way of German, probably first entering English in the word Ursprache (referring to a hypothetical 'first speech', the first language ever spoken by mankind).