The Greeks, like the Romans, used letters for numbers, but they used their own alphabet, and they used it differently. Alpha = 1, beta = 2, … iota (the ninth letter) = 9, kappa = 10, lambda = 20, mu = 30… sigma = 90, tau = 100, upsilon = 200, phi = 300, etc. To form a number, you would take the letter for the ones place (if any), the letter for the tens place, and so on, and added them all together. So 223, for instance, would be upsilon lambda gamma (I’m unsure of the order, there). The Hebrews used a similar system, using their own alphabet (I’m not sure who got the system from whom). Since any combination of letters could be either a word or a number, it became tempting to look for patterns in the numbers associated with words, and forms of numerology were very popular with both the Greeks and the Hebrews.
The ancient Mayans, like the Arabic system, had place value, but they used base 20 and only three symbols: A dot, a horizontal line, and something that looked like an Easter egg. You formed the digits from 1 to 19 using dots and lines: A single dot was the symbol for “1”, two dots for “2”, four dots for “4”, etc. Whenever you would have five dots, you replace them with a line. So the numeral for “10” would be two hoizontal lines, and “17” would be two dots on top of three horizontal lines. The Easter-egg thingy was zero, and numbers larger than 20 were formed using a place-value system very similar to how we make numbers larger than 10.
And the Babylonians used little wedge-marks (called cuineform) for all of their writing, as muttrox said (that being the easiest sort of mark to make in wet clay), but I don’t remember how in particular their number system worked.