"Twinking" is the general term for giving items to lower-level characters who can make better use of them. Many will be usable by any character you create, but occasionally, there will be some items (class-specific ones, in particular) that won't be useful to any of your characters if you've got a high-level character of that class. If that happens, just give it to a friend or sell it off in the Auction House - there isn't much point to keeping those, except for...
LLD (Low-Level Dueling)
In Diablo II, PVPers came up with a concept called Low-Level Dueling. They'd set a max level limit for the characters, which also limited the power level of items you were dealing with. If/when PVP is added to the game, LLD may become popular again. If that happens, there may be some low-level items that become particularly valuable, just for the fact that they are very powerful for their level requirement.