Well, some Coke crates are old and some are not as old. They were really used through the late 80's to early 90's in some areas. The value will depend on the overall shape of the crate and how well preserved the markings are.
There have been numerous crates. Some have partitions in them for the bottles. Later ones are without the partitions so cartons can be placed in them. I don't have a listing for any of the newer wooden cases from the 60's on. However, I know that ones in good shape seem to sell for $5-$25 at flea markets. Wood cases from the 50's back to the 30's are only valued from $10-$50. 1920's and earlier cases are valued from $85-$225.
Keep in mind that all pricing is subject to demand. You may do a whole lot better in an online auction. If people want something, they will gladly pay for it.
This is kind of a rough guess on these. Without more information, it is hard to say exactly what you can get for your crate. Good luck!