I've done some extensive analysis of number systems (almost enough to write a book on the subject) and come to the conclusion that the best are senary (6) and quaternary (4). Six has all the benefits of twelve, save the extra divisor of 2 (and thus 4), but that is easily remedied by use of the square (36) when required. Quaternary may seem an odd choice, but the square is 16, so one naturally learns hexadecimal without doing hardly any extra work --you just pair up the digits.
If your curious, duodecimal and octal come in after these and decimal falls to fifth place, which is fitting since its main advantage is divisibility by 5. :-)
Interesting. I always thought base 16 was the only suitable number system. Base 2 is the only justifiable one, since base 1 is not much fun. Squaring base 2 twice to get a fair amount of information in a single column seems to just make sense. What are the downsides of 16?
If your curious, duodecimal and octal come in after these and decimal falls to fifth place, which is fitting since its main advantage is divisibility by 5. :-)