Part of the rules I would like clarification on:

As a bonus action, you can move the sphere up to 30 feet. If you ram the sphere into a creature, that creature must make the saving throw against the sphere's damage, and the sphere stops moving this turn.

Question: If I ram a creature with the sphere, does the sphere end on the same 5x5 square/tile as the creature (sharing the space), a neighboring square/tile (next to the creature), or do I get to choose?

I think it occupies its own space. It doesn't state that it can be in the same space as a target like swarms.

 Full rules of Flaming Sphere just for reference.

It doesn't say that it can be in the same space as another creature.
It requires an unoccupied space when first cast.
It deals damage to creatures within 5ft (at the end of their turn].

All in all I agree with Wysperra, the sphere ends up adjacent to the creature..

I agree with the premise that it stays adjacent to the creature it smacks into, but I don’t think the fact that it doesn’t say that it can be in the same space as another creature is all that important. There is no general rule that indicates a problem with a spell effect or an object sharing the space with a creature other than the spell requiring an unoccupied space for the initial casting..

Also, don’t use this on drow. They will shut it down with their innate darkness spell.

I would rule it as occupying the last space it was in before it rammed a target. So would be adjacent. 

Thanks all! This will make it much easier to use against enemies that are in melee with teammates without burning my friends!

So Flaming Sphere doesn't do damage on the caster's turn when it is cast?  For the first round, it would  only  do damage at the end of the the turn of any creature who didn't have the  ability or good sense to get aways from being within 5ft of it at the end of the creature's turn?

And then on subsequent turns during the duration, it could be rammed into creatures as a bonus action and would do damage via ramming (and that is the primary way it inflicts damage) an  it would also do damage to any creature who ends its turn within 5ft of it (if the creature lacked the ability or good sense to move away from it)?  

How are spells the do damage do damage at the beginning of affected creatures' turn (like Moonbeam) different in the way they work from spells that do damage at the end of affected creatures' turns?  (what's the difference mechanically, in those 2 wordings and what are the implications?)

Many spells do not do damage immediately. Yes, flaming sphere is one of them.

The difference between damage at the beginning of a turn and the end is that damage at the end gives the opportunity for the creature to move on its turn before it takes damage. Damage at the beginning gives the creature no opportunity to move before it takes damage (baring any abilities to move on other creatures' turns). One could argue that damage-at-end-of-turn spells are much more valuable as soft control than damage unless your group also has a way of locking down a creature.

On the turn of creation, the caster can move it as a bonus action.

"As a bonus action, you can move the sphere up to 30 feet. If you ram the sphere into a creature, that creature must make the saving throw against the sphere's damage, and the sphere stops moving this turn."

Then if anything ends its turn next to it, it takes damage.

So possible two opportunities to do damage in a round.

Quote from Sangy >>

So Flaming Sphere doesn't do damage on the caster's turn when it is cast?  For the first round, it would  only  do damage at the end of the the turn of any creature who didn't have the  ability or good sense to get aways from being within 5ft of it at the end of the creature's turn?

And then on subsequent turns during the duration, it could be rammed into creatures as a bonus action and would do damage via ramming (and that is the primary way it inflicts damage) an  it would also do damage to any creature who ends its turn within 5ft of it (if the creature lacked the ability or good sense to move away from it)?  

How are spells the do damage do damage at the beginning of affected creatures' turn (like Moonbeam) different in the way they work from spells that do damage at the end of affected creatures' turns?  (what's the difference mechanically, in those 2 wordings and what are the implications?)

 Wysperra is correct. You can cast it as an action then use your bonus action to move it to ram a target for the damage the same turn. If you can place it where either the target cannot move away before they end their turn (blocked in somewhere) they take damage again.  Or next to an ally so that moving could cause an Opportunity Attack (so possibility of damage moving or not moving)