Well, probably whenever you have something to sell!
Joking aside, finding the best time to sell something on ebay is an important answer to find. If your auctions expire at a time when most of your potential buyers are going to be asleep, then you will likely earn a lot less on your sale. If you even sell it at all!
The goal should be to time the ending of your auction so that you know most of your buyers will be available to bid during the last hour or so of the auction. Saturdays and work days are usually bad because buyers have other things more important than to buy your item!
The best time will vary depending on what type of items you are selling. But most Ebay experts agree that generally speaking the best time to end an auction is from 6-9pm EST. This means that your US buyers will see the auction ending from 3pm(west coast)-9pm. Since sunday evenings are very often spent at home without much going on, you will find that many of your buyers will there to bid on your auctions.
Since normal ebay auctions last 7 days, you will need to list it the same time you want it to end - only one week earlier. If you aren't going to be home Sunday evening, you can always use the scheduled listing feature. They do charge a small fee for this, but it may be worth it.
Bonus tip: You can also do a 10-day listing starting on Thursday evening. This will cause your ebay auction to end on Sunday evening and your items will be seen by prospective buyers for two weekends. The extra exposure may be helpful.
Good luck and happy selling!
Interested in finding out more about selling your stuff on ebay Bob also writes about learning how to sell on ebay.