It certainly existed in Asia. In Nepal in particular, the kings wore a jewel and feather crown called a shreepech (clearly visible http://www.reuters.com/article/us-nepal-crown-museum-idUSBRE82I0LJ20120319). The caveat here is the monarchy in Nepal was highly influenced by several hundred years of contact with British colonial rule in neighboring India. Outside of the monarch, the hereditary prime ministers of the Rana family wore similar crowns often posing with regalia intended to mimic european nobility.

If by crown you mean the concept of a headdress that conveyed rule, power or status, then this has been in use for thousands of years by civilizations of all sorts. The Egyptian "Hedjet" crown dates back to early dynasty periods ultimately becoming the "Pschent" following the unification of upper and lower egypt. Likewise the Persians used a "Diadem". Similarly the word "Taj" as used by the Mughal rulers translates as crown (good link: http://intellectualpost.com/royal-insignia-of-the-delhi-sultans-and-mughals-taj-crown/). Likewise the Aztecs also had their own (http://www.bbc.co.uk/news/world-latin-america-17878130)

This is of course a small snapshot with many other examples existing from other civilizations and cultures as shown by some of the people who have already posted on this.

It is interesting to note, the concept of a headdress in human societies denotes rule, power or status across the board and across very large time scales.

I'm from Okinawa, Japan, which was its own little Kingdom before it was taken over. Our King certainly had a crown that I'm sure was influenced by Chinese culture. I could only find a photo of one from this local news site: http://ryukyushimpo.jp/news/prentry-205927.html

Nobles also had hats that looked like bento-boxes with specific colours to indented their rank.