It seems that up until armour became commonplace for profesional soldiers, one would throw whatever was handy. Rocks, spears, maces, even swords in some cases.
However, it does not seem like dedicated throwing axes where a big hit.

One reason could be compability with the other equipment in use. In a shield wall context, getting a hit past the enemy shields could be hard. Spears would be more likely to slip through small openings. Further more, a short axe like the francisca would not serve very well as a hand weapon in a shield wall, while a spear can be used for stabbing as well.

In later periods, when plate armour dominate, there isn't much point in throwing stuff at all.

I realize that this is an SCA-ism, so please don't mistake this for historical commentary. It's just an observation.

Hand axes are marvelous tools for hooking and displacing shields, so that spears behind the shieldwall and do their work. I carry a two small axes (one in my hand before the battle begins, and one tucked in my enarming straps) and a short sword.

I fave found that throwing axes in coordinated volleys is ineffective because the enemy sees it coming and turtles up. behind their shields. I suspect the same would be true for arrow volleys.

What works far better is to wait for a lull in the fighting, look for an opponent who isn't scanning or is distracted, and fire an axe at his face.

I also love to throw real axes, one of the cool (or scary) things about thrown weapons is that they bounce in weird ways, and there's no good way to get hit with a thrown axe. The bit might skip off of your helmet, fly left at a right angle, and the handle could break the nose of some random dude behind you. I can only imagine what hundreds of axes thrown at once would to to a poorly armored fyrd.

They don't work in the SCA context largely because there's not enough of them being thrown, and people aren't really afraid of taking an axe to the face, so the psychological element isn't there. Of course I've kept archers and spearmen ducking for cover over and over by pump faking, so there's something to be said for the fear factor.

Our first experiments went poorly because everyone instinctively threw at the opponent directly opposite them. Some things that make volleys better are throwing over the first few ranks so that people who feel safe get whacked, and throwing axes diagonally to your right, which goes into the enemy's less shielded sword side.

Throwing the axes sidearm seems to work better against a shallow formation like a shieldwall, because you tend to error left and right as opposed to up and down. If you miss your mark, you'll probably hit the guy next to him. An overarm throw is great against big blocks of infantry, but tends to sail right over a shallow shield wall.

Again, just observations and totally ahistorical.

Not Western European, but here are some pages with information on the fighting axes and hammers popular in Eastern Europe and the Steppes, many of which appear like they could be effective throwing weapons:

http://www.redkaganate.org/martial/weapons/axehung.shtml

http://www.redkaganate.org/martial/weapons/axerus.shtml