The distinction between aggregation and composition depends on context.
Take the car example mentioned in another answer - yes, it is true that a car exhaust can stand "on its own" so may not be in composition with a car - but it depends on the application. If you build an application that actually has to deal with stand alone car exhausts (a car shop management application?), aggregation would be your choice. But if this is a simple racing game and the car exhaust only serves as part of a car - well, composition would be quite fine.
Chess board? Same problem. A chess piece doesn't exist without a chess board only in certain applications. In others (like that of a toy manufacturer), a chess piece can surely not be composed into a chess board.
Things get even worse when trying to map composition/aggregation to your favorite programming language. In some languages, the difference can be easier to notice ("by reference" vs. "by value", when things are simple) but in others may not exist at all.
And one last word of advice? Don't waste too much time on this issue. It isn't worth it. The distinction is hardly useful in practice (even if you have a completely clear "composition", you may still want to implement it as an aggregation due to technical reasons - for example, caching).