Using two swords wasn't common, but there are Bolognese fencing treatises that show this. Marozzo's treatise shows two swords starting at capitolo 76 (under "sword and weapons"), Mancilino shows two swords, and di Grassi also shows two swords. There are also Filipino martial arts that involve using two edged weapons, but I'm not very familiar with them.

In a one on one fight, it's not a huge advantage against single sword, but it's useful in fights against multiple opponents where you don't worry about projectiles and pole weapons. In pretty much all situations in which you can carry one, a large shield has a near absolute advantage over a second sword. Two swords are useful in a specific context.

Di Grassi's introduction to the use of two swords:

There are also used now adays, aswell in the schools, as in the lists, two Swords or Rapiers, admitted, and approved both of Princes, and of the professors of this art, for honorable and knightly weapons, albeit they be not used in the wars. Wherefore I shall not vary from my purpose, if I reason also of these, as far as is agreeable to true art. To him that would handle these weapons, it is necessary that he can aswell manage the left hand as the right, which thing shall be (if not necessary) yet most profitable in every other kind of weapon. But in these principally he is to resolve himself, that he can do no good, without that kind of nimbleness and dexterity. For seeing they are two weapons, and yet of one self same kind, they ought equally and indifferently to be handled, the one performing that which the other does, and every of them being apt aswell to strike as defend. And therefore a man ought to accustom his body, arms and hands aswell to strike as defend. And he which is not much practiced and exercised therein, ought not to make profession of this Art: for he shall find himself to be utterly deceived.

The one I'm most familiar with is Miyamoto Musashi's Ni-ten Ichi Ryu that he discusses in the Book of Five rings. His logic behind it comes down to mobility and flexibility. Most orthodox kendo and iaido schools teach single sword fighting with a two handed grip. Musashi felt this was limiting in two distinct ways. First, a two handed grip limits your range of motion and slows positional changes. A two handed grip is less fluid than a single handed one. The second and more philosophical reason was that most samurai carried two blades (Katana and wakizashi) but only fought with one. This struck Musashi as a waste, and bothered him that someone would die without using every tool at their disposal.

One final oddity of Ni-ten Ichi Ryu is that, at least as training (and according to a few accounts of musashi's later duels) it encouraged the use of two long blades instead of the more standard long and short.

As for your practicality question that's a little trickier. Musashi himself used two sword figthing to great effect. He was an undefeated duelist (not all were fought with two swords. His most famous waa fought with a boat oar after all), and was noted for his defense when using two blades being exceptionally good.

That being said, shields were not widely used in Japanese warfare, so it's hard to say how his style would have faired against it. Musashi was also noted for being a very large man, which would have enabled him to use dual long blades more proficiently than his students.

The Florentine style of fencing uses a sword and dagger, but I am not familiar enough with it to say any more than that.

Sources:

The Lone Samurai: The Life of Miyamoto Musashi by William Scott Wilson.

The Book of Five Rings by Miyamato Musashi.