Did any armies systemically favor axes/hammers over swords?

Fantasy fiction, art and films tend to over-emphasize swords, compared to what was historically used, as they both take more effort and metal to make, and more skill to use properly, than spears, clubs, maces, axes or polearms. Even contemporary art depictions of battles tend to overemphasize swords for their symbolic value and because they tend to focus on nobles rather than the common levies.

The most common pre-gunpowder weapon was probably the spear, and not necessarily a particularly long one. Pre-gunpowder cavalry tended to use spears or lances as their main weapons. Also common for medieval armies would be a mix of whatever men had, and most common men often did not have swords, using instead spears, maces, clubs, polearms, or weapons which were also their daily tools, such as axes, pitchforks or other various farming poles with metal heads. They would use what they had, and for medieval levies in particular that would tend to be a mix of types.

Some uniformly-armed groups of professional warriors also used weapons other than swords or spears. Famous examples include Anglo-Saxon Huscarls with two-handed axes and Swiss Halberdiers. Norse warriors would use axes and spears, in addition to those who had swords.

Even princes and wealthy nobles often used weapons other than swords and lances, particularly after heavy full-body armor made swords less useful. Maces, picks and axes tend to be more capable of hurting a man in full plate armor than a sword.

Aztecs and other American cultures favored clubs. See the macana (Taino) or the Aztec machuahuitl:

These clubs were studded with obsidian, and so were sharp and could be used to slice like a sword. But they still lent themselves to a different kind of combat:

The maquahuitls were incredibly strong, and the Spanish claimed they could chop the head off a horse with one blow. They were sharp and the Aztecs knew how to use them. They could not thrust like a sword, and so they lent themselves to a different type of warfare.

If you didn't have obsidian, it was common for Aztecs to use wooden clubs or maces:

The maquahuitl could be used as a club, but other types of clubs were used. The cuauhololli was a mace made of wood with a ball at the end. It could be used to smash and crush. Various other types of clubs were commonly used, sometimes just made of wood, other times with embedded stone as the maquahuitl.

Aztecs also used spears, lances, slings, bows and arrows, and atlatls. While there was metallurgy in pre-Columbian America, it wasn't really used to produce weaponry like swords and knives. Perhaps this is because obsidian was so effective.

As an aside, Franks had their franciscas, though they would also use swords after hurling the franciscas.

Source for quotes: Ancient Aztec Weapon

The french maillotins (wiki only in french) led a revolt in Paris, and consisted of several thousands of armed men. They managed to keep Charles VI imprisoned (in his palace ofcourse) for some time and held on to the city for about a year. Their name comes from the lead hammers of the weapons-depot of the city that where used to defend the walls from attackers.

The Huscarls of the Scandinavians and eleventh century Angle-Saxons fought with two handed Dane-axes. The Varangian guard of the byzantine emperors used the same weapon. Though an elite guard they numbered 6000 in the beginning. (Harald Hardrada, the guy who fought Harold Godwinson and his previously mentioned Huscarls for the throne of England was a Varangian btw).

Many ancient germanic warriors chose to wield clubs. some of them where depicted on Trajans column possesing swords but chosing to wield clubs (click next till number 17).

Among the emperor's strike force rushing along the Lower Moesia in scene 36 of the Column, a club-wielder is perhaps the most eye-catching figure. (...) In his left hand he holds a shield and on his right side a sword hangs from the baldric. The club in his right hais thin at the angle and widens towards the tip. Like other men in the scene, he holds his weapon ready; he will fight with the club first and only then with the sword.

The Bastarnae where famous for fighting bare chested with the Falx, shown below.