Funny you should ask. I just made a batch of hard-boiled eggs yesterday, and the Sell By date is Aug. 13. When put in the pot, the wider end pointed up, but they didn’t float to the top. It just means that they aren’t entirely fresh. If they float to the top of the water, it’s probably best to get rid of them.
llewis also brings up a great tip for checking if they are still good or not…crack one open and smell it. If it appears to be okay, I recommend just cooking it thoroughly. I wouldn’t eat an egg sunny-side up unless it is fresh.
Ame_Evil also brings up a valid point…it depends on how you store them. Mine are in a very cold refrigerator. In England, they are sold on a non-refrigerated shelf in stores and some people leave them out. I suspect that they are more prone to going bad more quickly. This may be why the Brits have a pretty big concern about salmonella.