Maybe not quite what you are looking for, but Alexander the Great could rarely refrain from joining the fray. It's been a while since I've read about Alexander's campaigns and my books aren't with me, so I can't think of any examples where he was at the head of the cavalry, just numerous examples of leading from the front and being involved in battles/skirmishes. Off the top of my head, he took the charge while assaulting fortifications many times. When Alexander did this, it was almost always to inspire his troops and drive them to action.

Arrian 4.10:

Alexander in person led his forces against a certain city of the Brachmans, because he ascertained that some of the Mallians had fled for refuge into it. When he reached it, he led his phalanx in serried ranks close up to the wall on all sides. The enemy seeing that their walls were being undermined, and being themselves repulsed by the missiles, abandoned the walls, and having fled for safety into the citadel, began to defend themselves from thence. A few Macedonians having rushed in with them, turning round and drawing together into a close body, drove some of them back and killed five-and-twenty of them in their retreat. Hereupon Alexander ordered the scaling-ladders to be placed against the citadel on all sides, and the wall to be undermined ; and when one of the towers, being undermined, fell down, and a part of the wall between two towers was breached, and thus rendered the citadel more accessible to assault in this quarter, he was seen to be the first man to scale the wall and get hold of it. The other Macedonians seeing him were ashamed of themselves and mounted the ladders in various places. The citadel was soon in their possession.

And of course there was when he got seriously injured assaulting a town, receiving a projectile in the lung:

Alexander, thinking that the men who carried the ladders were too slow, snatched one from a man who was carrying it, placed it against the wall, and began to mount it, crouching under his shield. After him mounted Peucestas, the man who carried the sacred shield which Alexander took from the temple of the Trojan Athena and used to keep with him, and have it carried before him in all his battles. After Peucestas, by the same ladder ascended Leonnatus the confidential bodyguard; and up another ladder went Abreas, one of the soldiers who received double pay for distinguished services. The king was now near the battlement of the wall, and leaning his shield against it was pushing some of the Indians within the fort, and had cleared that part of the wall, by killing others with his sword. The shield-bearing guards becoming very anxious for the king's safety, pushed each other with ardour up the same ladder and broke it; so that those who were already mounting fell down and made the ascent impracticable for the rest. Alexander then, standing upon the wall, was being assailed all round from the adjacent towers; for none of the Indians dared approach him. He was also being assailed by the men in the city, who were throwing darts at him from no great distance; for a mound of earth happened to have been heaped up there opposite the wall. Alexander was conspicuous both by the brightness of his weapons and by his extraordinary display of audacity. He therefore perceived that if he remained where he was,he would be incurring danger without being able to perform anything at all worthy of consideration; but if he leaped down within the fort he might perhaps by this very act strike the Indians with terror, and if he did not, but should only thereby be incurring danger, at any rate he would die not ignobly after performing great deeds of valour worthy of recollection by men of after times. Forming this resolution, he leaped down from the wall into the citadel; where, supporting himself against the wall,he struck with his sword and killed some of the Indians who came to close quarters with him, including their leader, who rushed upon him too boldly. Another man who approached him he kept in check by hurling a stone at him, and a third in like manner. Those who advanced nearer to him he again kept off with his sword; so that the barbarians were no longer willing to approach him, but standing round him from all sides whatever any one happened to have or could get hold of at the time.

Meantime Peucestas and Abreas, the soldier entitled to double pay, and after them Leonnatus, being the only men who happened to have scaled the wall before the ladders were broken, had leaped down and were fighting in front of the king. Abreas, the man entitled to double pay, fell there, being shot with an arrow in the forehead. Alexander himself also was wounded with an arrow under the breast through his breastplate into the chest, so that Ptolemy says air was breathed oat from the wound together with the blood. But although he was faint with exhaustion, he defended himself, as long as his blood was still warm. But the blood streaming out copiously and without ceasing at every expiration of breath, he was seized with a dizziness and swooning, and bending over fell upon his shield. After he had fallen Peucestas defended him, holding over him in front the sacred shield brought from Troy; and on the other side he was defended by Leonnatus. But both these men were themselves wounded, and Alexander was now nearly fainting away from loss of blood. For the Macedonians had experienced great difficulty in the assault also on this account, because those who saw Alexander being shot at upon the wall and then leaping down into the citadel within, in their ardour arising from fear lest their king should meet with any mishap by recklessly exposing himself to danger, broke the ladders.

Ramesses II claimed to have lead charges at the Battle of Kadesh. If he did or not who knows.

Given king's tendency to exaggerate their claims this one is going to be tricky to prove unless the king in question ended up dead.

If James IV wasn't at the front of a charge at Flodden Field he was certainly far enough forward to end up dead.

Richard III appears to have lead the charge that got him killed. Constantine XI might have died leading a charge

As a tactic it isn't crazy. A fair number of cultures expected their leaders to fight. Those leading smaller forces would have had little choice but to fight. Once battle was joined the ability to communicate with your forces was often limited so the loss of communication wasn't always as big a problem as it seems.

A king taking the lead may help with moral but it also forces any wavering supporters to make up their mind. If your king charges and your clan, warband, army doesn't you'd better hope that he loses and his enemy is really rather merciful (wasn't unknown for a king's personal household to be the only troops he could have a solid degree of faith in).

As /u/geniice points out, in many ancient cultures this was more or less expected of a general. It was a staple of Greek warfare from the Homeric world down to the Macedonian conquest; Alexander the Great set a new benchmark of suicidal bravery that became the ideal for all Hellenistic kings of the period that followed. To add to the examples of /u/ScipioAfricanvs, at the battle of the Granikos Alexander led the cavalry and nearly died when a Persian noble struck at his head with a sword.

The Greeks were keenly aware of the conflict between the two roles of the general - providing effective leadership and giving the right example. However, they tended to err on the side of the latter. As modern scholars like E.L. Wheeler have put it, they preferred the "soldier's general" command style, where the commanding officer shares in the hardships and dangers faced by his men in order to inspire them to great deeds of endurance and valour. Needless to say, a very large number of Greek generals died in battle.

One example that is particularly relevant to your question is that of the Theban Pelopidas. At the battle of Kynoskephalai, in 364 BC, he was directing his men onward when he spotted his mortal enemy Alexander of Pherai in the ranks of the enemy army. He rushed forward with no regard for his own safety, and Alexander's bodyguards cut him down. However, since Pelopidas' troops were very fond of him, his death actually whipped them into a frenzy, and they charged and butchered Alexander's entire army, pursuing the fleeing remains until the fall of night. For the only surviving account of this battle, see Plutarch, Life of Pelopidas, 32.

One reason to keep in mind why this isn't quite as crazy as it sounds is that in the past, a lot of soldiers had to provide their own equipment. This means that most soldiers are wearing whatever relatively cheap armor they can get, whereas the king is fitted out in the finest armor and weapons that money can buy, making him far better protected than most of the people he's fighting.

Some historical examples have already been mentioned, and I would like to add, that nowadays in certain armys, influenced by certain military cultures, you still have this kind of leadership. A lot of high-ranking officers of the iranian revolutionary guards died at syrian frontlines, and one syrian general is notoriously famous for fighting alongside his soldiers.