Settle in for a good thread.
I think you'll find several camps. I think you'll find that the PHB and the FAQ have some very different things to say about the subject. I think you'll read in this thread many opinions on what is and what should never be (to borrow from Zeppelin).
What the heck... I'll start off with my own conclusions.
All the melee weapons on Table 7:5 in the PHB are classified as light melee weapons, one-handed melee weapons, and two-handed melee weapons. These classifications are part and parcel of the weapon. Regardless of any other factors, by the PHB rules, a greataxe of any size is a two-handed weapon. Under certain circumstances (most notably, item size category not matching wielder size category) any particular greataxe may be wielded in one hand, two, or may not be wieldable at all. Nevertheless, it remains a two-handed melee weapon as defined on page 113 of the PHB. Weapon Size: is a totally different property of the weapon and is completely independent. It is also described on page 113 of the PHB.
As you can read from table 7:5, the lance is a "two-handed melee weapon." Page 113 of the PHB rules that when wielding "two-handed melee weapons" apply 1 and 1/2 times the wielders STR bonus to damage. The special rules text for the lance says "while mounted, you can wield a lance with one hand." This is very different than saying "while mounted, the lance counts as a one-handed melee weapon." The actual rule text for lances overrides the normal condition expressed in the first sentence of the rules for two-handed melee weapons which says, "Two hands are required to use a two-handed melee weapon effectively." The lance even while being wielded in one hand remains a two-handed weapon, and deals damage as a two-handed weapon, because, as discussed above... the lance is always a two-handed weapon, and by the rules for two handed weapons, they do not deal differing amounts of damaged based on how they are wielded.
The FAQ more or less ignores the rules as written in the PHB and says that weapons do not have permanent category as described in the table 7:5 and the rules text on page 113, but rather, their qualities are purely determined by how they are wielded... except that the FAQ seems to forget that other qualities of the weapon are determined by the light/one/two classification (such as hardness and hp)... and it would seem a bit strange that the hp of your weapon could change by adding or removing hands from it's grip... or by handing it to a different sized creature.
That's my view on how it is. How should it be? That's a different matter. I don't have a simple answer to that because I think to consider it properly would require a detailed analysis of two handed styles versus two weapon styles versus mounted combat styles in conjunction with a possible reworking of feats and prestige classes. Furthermore, any such analysis and results would be firmly in the realm of house rules in my opinion.
