What were the typical uses of these three types of long weapons?
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[li]Spear–Jabby/stabby/throwing thingee. Knife onna stick. Used in war & hunting. May be fitted with a crossbar at the top, to keep enemies/game from forcing their bodies up the shaft & doing nasty things to you. Some people are just ungrateful, I guess.[/li][li]Pike–like a spear, but longer. No throwing. War weapon only. May have a hook attacked for yanking knights off their horsies.[/li][li]Halberd–Hybrid pike/battleaxe. War only. Very nasty inna fight. Definately will have a hook thingee for relieving the horsies of their burdens.[/li]
You didn’t ask, but–
[li] Godentag. Flemish weapon. Long wooden club with an awl-like spearpoint at the end. May have rows of wooden/metal spikes running the length. Stabby/smashie thingee. Cheap to make, very nasty inna fight.[/li][li]Lance–long spear/pike, used from the saddle of a horse. Charge at hapless oaf at high speed, ram him with lance, oaf-kabob.[/li][/list]
Me? I prefer flyswatters. 
An english Yeoman with a long bow trumps all of them!
Oh, pluck yew.
Only if he’s standing far enough away. Archers make just as nice kebabs as anyone else.
Pole arms are sort of a tough one since there are so many. But here’s a few more generalities.
Spears are really just like Bosda says: a knife on a stick. Some are good for throwing, others for holding and stabbing with. Still with us today in the form of rifle and bayonet.
Pikes, like Bosda says, are generally much longer than spears and only for war. Whereas a hunter might use his spear for bringing down game, a pike is too big to do so. It was usually between 15 and 20 feet. Pikes were only effective when used in tightly packed phalanxes. Just to make things more confusing, there were “half-pikes” that were basicaly spears.
Halberds are where it gets very confusing because of all the different heads that one might find on a long spear shaft and the wide terminology associated with them. But the basic halberd was the axe-head on a spear. Some were double-bladed, some had a hammer type head backing the blade side, others had a spear tip in addition. The ones with hooks were usually called bills and were descended from tree pruning tools (one guy uses his billhook to pull a branch down while another uses his billhook blade to cut it). But of course, some halberds might have hooks. In an early rennaisance army, a halberd would be a mark of an NCO while all the others in a block of infantry were armed with pikes.
I’ll leave it at that.
Of the lot of em, I’d want to be armed with the godentag.
Cheap & nasty.
Like my High School’s Homecoming Queen, way back when.
AH! Memories… 
I think even up to Napoleonic times often sergeants and the like carried halberds as symbols of leadership, even while the grunts were armed with brown bess muskets and bayonets.
Though these probably had evolved down into something shorter and easier to carry than full length medieval weapons, as they were used more as symbols (and probably to thwack reluctant grunts) than in a massive block of pikemen.
Some piccies: Halberd, Bill and Poleaxe