When should I accept a parameter of Iterable<T> vs. Collection<T> in Java?

Many of the collection types existed before Iterable<T> (which was only introduced in 1.5) - there was little reason to add a constructor to accept Iterable<T> as well as Collection<T> but changing the existing constructor would have been a breaking change.

Personally I would use Iterable<T> if that allows you to do everything you want it to. It's more flexible for callers, and in particular it lets you do relatively easy filtering/projection/etc using the Google Java Collections (and no doubt similar libraries).

An Iterable produces Iterator objects. An Iterator object, by definition, iterates. Notice, that the Iterator interface makes no promise as to how many times next() can be called before hasNext() returns false. An Iterator could possibly iterate over Integer.MAX_VALUE + 1 values before its hasNext() method returns false.

However, a Collection is a special form of Iterable. Because a Collection cannot have more than Integer.MAX_VALUE elements (by virtue of the size() method), it is naturally presumed that its Iterator objects will not iterate over this many elements.

Therefore, by accepting a Collection rather than an Iterable, your class can have some guarantee over how many elements are being passed in. This is especially desirable if your class is itself a Collection.

Just my two cents...