Why do some analog clocks with Roman numerals have '4' as 'IV,' while others have 'IIII'? This is one of those questions where no one seems to have a definitive answer, and probably no one ever will. What we do have is a handful of competing theories, some with plenty of holes and others that might just be true. You'll have to pick the one that sounds best to you and roll with it.
Once upon a time, when Roman numerals were used by the actual Roman Empire, the name of the Romans' supreme deity, Jupiter, was spelled as IVPPITER in Latin. Hesitant to put part of the god's name on a sundial or in accounting books, IIII became the preferred representation of four. Of course, IVPPITER wasn't being worshipped much by the time clocks and watches replaced sundials, but clockmakers may have stuck with IIII just for the sake of tradition.
In another blow to the Jupiter theory, subtractive notation—where IV, instead of IIII, represents four—didn't become the standard until well after the fall of the Western Roman Empire (and the numerals we use now are an even more modern set). It's likely, then, that IIII was used on sundials (and everywhere else) simply because that was the proper numeral to use at the time, and not for fear of divine retribution.
Once subtractive notation came onto the scene and a choice was available, to V or not to V became a question every clockmaker had to answer for themselves. Some adopted the newfangled IV because it was the new standard, but others hung on to the traditional IIII.
IIII might have stuck around because it's easily recognizable as four. IV involves a little math. Yes, it's just one simple subtraction operation, but keep in mind that when subtractive notation really caught on in the Middle Ages, the majority of people weren't literate or numerate. Subtraction was a lot to wrap the head around. On top of that, IV and VI might have been easily confused by the uneducated (likewise with IX and XI, which is why nine was sometimes represented by VIIII).
Using IIII may have also made work a little easier for certain clock makers. If you're making a clock where the numerals are cut from metal and affixed to the face, using IIII means you'll need twenty I's, four V's, and four X's. That's one mold with a V, five I's, and an X cast four times. With an IV, you'd need seventeen I's, five V's, and four X's, requiring several molds in different configurations.
King Louis XIV of France supposedly preferred IIII over IV, perhaps for the same vain reasons Jupiter wouldn't want two letters from his name on a sundial, and so ordered his clockmakers to use the former. Some later clockmakers followed the tradition, and others didn't. The problems here are that this story is told in connection with many other monarchs, and IIII was used also in areas where there was no king with an IV in his title to object to the subtractive notation.
One more reason to use IIII is that it creates more visual symmetry with the VIII opposite it on the clock face than IV does. Using IIII also means that only I is seen the first four hour markings on the, V is only seen in the next four markings, and X is seen only in the last four markings, creating radial symmetry. As we learned last year when pondering why display clocks are often set to 10:10, symmetry goes a long way in the clock world.