The Hebrew word for ten is eser עשר (and the masculine form is asarah עשרה). Does this number derive from an earlier word?
Klein follows the BDB, and writes about the root עשר:
The orig. meaning of this base prob. was 'gathering, collection, union'. cp. Arab. 'ashara (= he formed a community), 'ashirah ( = tribe), ma'ashar (=a group of ten men). Accordingly, Heb. עשר (eser), Arab. 'ashr, etc. prob. meant orig. 'a group collection', whence 'a group of ten', and ultimately 'ten'.
Rav Hirsch (Bereshit 14:20) follows the same line of thought, and mentions that other similar sounding roots also have related meanings: אסר, אצר, עצר, אזר, עזר.
Steinberg, in Milon HaTanach, has a different theory. He says that עשר is related to עצר, meaning "to stop". He therefore writes that eser got it's name because it is where you "stop" counting (when you're counting on your fingers.)
Strong takes a slightly different approach. He writes:
A primitive root (ident. With ashar); to accumulate
Should we accept the connection with the words ashir עשיר - wealthy, and osher עושר - riches? At first we might reject this approach because one has the letter sin and the other has the letter shin. But we can see here that many Semitic languages have the "sh" sound in their word for ten: esher in Akkadian, `asharah in Arabic.
So to determine if there is a connection, we should use Horowitz's advice (and Lonnie's Biblical Hebrew teacher's), and see how each term is used in Aramaic. Ten in Aramaic is עסר (asar), where rich in Aramaic is עתיר (atir) - a term still used in Modern Hebrew.
So it would seem that Strong's theory is hard to accept. However, the Rabbis did make use the similarities between "ten (or tenth/tithe") and "riches" to provide a play on words.
Jastrow provides two examples. One is from Shir HaShirim Raba:
אם זכיתם תעשירנה ואם לאו תעשירנה - "If you deserve well 'you make her rich', if not 'you reduce her to one tenth'.
The other source, from Shabbat 119a and Taanit 9a would seem to provide an opposite message:
עשר בשביל שתתעשר - "Give tithes in order that you become rich".