You know what they say...if you have to ask...
In all seriousness, the answer is probably yes. In most cases, it is financially logical for you to insure your engagement ring.
Insuring an engagement ring typically costs 1-2% of the value of the ring, paid once each year. Some quick math tells us it would take 50-100 years of paying premiums for you to pay more in insurance than it would have cost you to replace your ring.
So unless you have a casual several thousand dollars laying around, it only makes sense to slap some insurance on that sparkler.
But just for fun, here's a little flowchart to help you decide: