Axes and swords have their own advantages, but I will personally favor the spear.
It's the quickest to learn, easiest to use, and most advantageous over the other melee weapons. The extra reach is very useful for keeping other combatants at bay, even if it might not be as fatal as a sword. Furthermore, they're easier to use while holding your guard.
Maces have their own benefits, with sheer crushing damage, but I'd still rank the sword slightly better than them. Axes, while having more chopping power, aren't as useful for parrying, and can't stab, so they also have disadvantages, compared to swords.
There are also daggers, which, while not very effective in a straight up fight, can end one before it even starts if the wielder is quick enough, or they get in a sucker stab.
Then there's warhammers, which, while delivering assloads of blunt trauma, still aren't as effective as a claymore. However, it does depend on the wielder. If somebody can swing a warhammer effectively, they're going to turn anybody that tries to fight them, unless the enemy has a spear, pike, or halberd, into mush.
Overall, polearms are probably the best melee weapons, in my opinion. Spears are easy to use and have many advantages, and halberds deliver the chopping force of an axe, as well as stabbing power, from a longer distance.
Well… polearms are superior to all but…
The damn bonk…