This one is an old chestnut that I somehow have managed not to be asked for a while. Here's the quotes at issue, Exodus 9:3-6 and 14:9 --

And the next day the LORD did it: All the livestock of the Egyptians died, but not one animal belonging to the Israelites died.

The Egyptians--all Pharaoh's horses and chariots, horsemen and troops--pursued the Israelites and overtook them as they camped by the sea near Pi Hahiroth, opposite Baal Zephon.

You know it by know -- the question is, where did Pharaoh get all the horses if they were all killed in the plague?

A standard solution cites Exodus 9:3 as specifying that the plague was on animals in the field -- any animals not in the field (i.e., in stables, like Pharaoh's horses certainly would have been) were not affected. But this does run aground on verse 19, which says that all of the livestock died.

A better solution recognizes that there is a certain misconception that the Ten Plagues were right on the heels of one another. But the #2 plague (frogs) probably took place in December ("frog season" there, as they would mate during the flood season which lasted until October, and then grow to sufficient size by December) and the #7 plague (hail) occurred in January, because, according to commentators familiar with Egypt's growing seasons, the barley was ripe and the flax was in blossom (9:31). Then of course by the time of the Exodus it was April. That gave at least 2-3 months for the Pharaoh to replenish his stables -- certainly no problem for a world power like Egypt, which could do that either by trade, conquest or by outright confiscation from the Israelites and other foreigners. Indeed it is the height of absurdity to suggest that Egypt -- perhaps the greatest power in the world at the time -- would not have the means to do this; it did not require "invasion" of another country but normal trade or confiscation from those already in the country or close by -- and it also requires no stretch to ask what happened to the dead animals; certain commentators seem to forget about the wide availability of slave labor; that Israel furthermore had flocks and herds later hardly negates any point that some portion was able to be taken from them.)

It should be noted, contrary to some undisciplined commentators, that this requires no exceptional length of time or stretching of the Biblical chronology. The plagues take place in this scenario over a mere 6 months. This involves no significant delay whatsoever, and appeals to texts that record Moses' age neglect the point that Moses would hardly have had more than one birthday over these few months (even if ancient persons were indeed able to precisely calculate their own ages, which was not often possible). Nor is it necessary to suppose that Pharaoh waited more than a few days to ask for the removal of the plague of frogs, once it became clear that his own magicians could do nothing to reverse it and once his own sense of honor had been broken sufficiently to make the request. The place for space is between the conclusion of one plage and the start of another, and the texts offer no time markers for those, save the ones that context (knowing the seasons) would provide for the knowledgeable reader. (The single example offered that the locusts ate what the hail did not destroy hardly indicates that the hail followed on the heels of the locusts, since the crops are obviously not going anywhere; any "regrowth" of vegetation is of no relevance, for it is hardly as though any regrowth would be counted as new plants! It is also absurd to claim that any delay would lessen the memory of the prior plagues -- as if such things were indeed so readily forgotten!)

As an added note, since we don't know exactly how many horses there were in the pursuing army, we might reckon that some of them were originally out on military work outside Egypt at the time of the plague. Whatever the case, there is no sufficient ground for dismissing the story outright. It should furthermore be recalled that the best-trained army in the ancient world, with horses and chariots and armor and weapons, versus a mixed crowd of untrained, unarmored, on-foot pastoralists, isn't any cause to wonder why, though outnumbering the Egyptians significantly, the Israelites were concerned: Such objections are made by "armchair" generals whose worst war wound has been a paper cut.)