http://languagelog.ldc.upenn.edu/nll/?p=2
In "Remember the First 100 Digits of Pi Using This Basic Technique" (mental_floss, 12/11/15), Caitlin Schneider describes a "memory palace" in which one can use letters to recall long strings of numbers.
You can do this with Chinese too, as described in this Language Log post, linking to this Wikipedia article.
Helvetica Baskin Robbins points out that Japanese numero-mnemonics has an advantage in that the numbers have different readings, thus allowing for more flexibility in coming up with zany ("quasi-nonsense"), memorable phrases to assist in recalling sequences:
0 = rei, zero. "O" is also used in mnemonics. Sometimes "wa" for ring is mapped to 0, but this can be confused with 8.
1 = ichi, hito.
2 = ni, futa. "Ji" is also used in mnemonics.
3 = san, mi.
4 = shi, yon.
5 = go, itsu.
6 = roku, mu.
7 = shichi, nana.
8 = ya, hachi. Sometimes "wa", similar to "ha" in "hachi" is mapped to 8, but this can be confused with 0.
9 = ku, kono.
While we're talking about Chinese and Japanese numero-mnemonics, I cannot help but mention a most intriguing chapter (number 5) in J. Marshall Unger, Ideogram: Chinese Characters and the Myth of Disembodied Meaning (University of Hawai'i Press, 2004): "How would a magician memorize Chinese characters?" Highly recommended, if you're interested in the sheer memorization of characters.
[h.t. Ben Zimmer]