An old, and rather silly paradox: Can almighty God create a stone so heavy that He cannot lift it? If He did create such a stone (the paradox goes) then there would be something that He could not do (i.e. lifting it), but that cannot be because (since He is almighty) there is nothing that He cannot do. Hence He did not (and will not) create such a stone—but therefore there is something that He cannot do (i.e. creating such a stone). Consequently (the paradox concludes) no such omnipotent being (a being for which nothing is impossible) could exist; but several replies are possible, most obviously that "omnipotence" should be defined in such a way that impossible things do not have to be done by omnipotent beings. The paradoxical reasoning can then be taken to be showing that such a stone is impossible—since an omnipotent being could move any possible weight of stone, so no such stone is a possible object. It is certainly hard to get any sense of what such a stone would be like (e.g. were it filling all of an infinite space, it could not then be lifted, but then it would not be too heavy, so much as too big to lift).
......God might even be contradictory (so powerful His powers transcend our mundane powers of linguistic description) of course, although I personally think of God as almighty in the sense of His being able to do (at least) whatever He wants with His Creation (which is at least this Cosmos) and presumably much more besides (although presumably God could not do what He did not want to do with His Creation, and the idea of God possibly wanting something that He does not actually want is rather obscure, whence the modalities are also obscure); but what strikes me about this paradox is how odd it is, to think of Him lifting stones at all (like He was like Hercules, only bigger)—far more impressive is His creation ex nihilo of a pebble. Now, traditionally God not only creates, but also at each moment keeps all created things in existence, which raises the question: Why bother with all of that (in the case of purely material objects, like stones) just to generate the phenomena sensed by sentient creatures; why not generate the latter directly? One theistic argument for Idealism (the topic of this fortnight's Philosophers' Carnival) is that material objects do seem a bit pointless (e.g. they might be less deceptive than mere appearances, but only if modern physics has got them very wrong).
......Creation itself seems a bit gratuitous though; so, one might ask: Could almighty God create an object that He did not have to keep in existence, from moment to moment, which was instead self-sustaining, to some extent? Maybe (since that does not seem to be contradictory), but God is also traditionally eternal in the sense of existing atemporally (a bit like numbers do), so it is hard to see what difference that would amount to. Still, for all we know God (and all Creation) exists more in the manner of a person—fully (if mutably) in the immense present—whence we might ask: Could almighty God create an object so self-sustaining that even He could not destroy it? He can create souls (as well as stones) it seems, and with such free will that even Satan is a possible object; and the giving of such freedoms, to His creatures, involves the voluntary limiting of (what we naturally regard as) His powers, within Creation (on this view of eternity), so maybe He could—such an object does not seem to be contradictory. Maybe, like the aforementioned stone, it is no more than a Philosopher's plaything, but such a perfectly indestructible object could conceivably be something that God would want to create (maybe our lovely Creator knows better than to be certain that Beings with powers akin to His, but of which He is, as yet, unaware, do not exist).