My question is this. If you draw a spell, such as counter spell, which requires you to cast it only when a spell has just been casted. However you are playing against the Troll, and Orge Cheiftan, who have no intentions of casting a spell. Can you simply drop the spell, on the space you are on, for someone else to pick up? As if you were dropping a 5th item because you can only carry 4? Or are you forced to keep it until you aquire another spell, and then cast counterspell on yourself, just to get rid of it, so you can get back to drawing a new spell each turn if you begin your turn without a spell. (Wizard ability)

We have been playing that you must hold on to it, until you can cast it, but this significantly cramps the ability of the spell caster. Also dropping the spell, would allow any chacacter to pick it up on the landed spot. Thoughts on this?

You're playing correctly. The only way to rid yourself of a spell is to cast it!

Also, you may know this already, but remember you can only cast the number of spells you had at the start of your turn. If you begin with two spells and gain a third, you can only cast two spells during that turn. Spells gained automatically at the start of your turn, such as via the Sage and Warlock's special abilities, count towards that total. Remember also that you can only cast one spell on an opponent's turn.

The only way to get rid of a spell is to cast it or if you are over your limit then you may discard one to the discard pile. See page 13 of the rulebook.

"If at any time a character has more Spells than his Craft

As the others said, you should try to get at least one more Spell.

If it is a Spell that you can cast, use it and then cast Counterspell on it to avoid being stuck with Counterspell indefinitely.

Spells have nothing to do with a characters Object Limit! The number of Spells a character may have is determined by his amount of Craft.