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Sara, the main concern I see here is you will have a card that is near the credit limit. When they determine your score for your credit report they look at how much available credit you have and how much you have actually used. Most people will tell you only to use a third of what is being offered. I can understand wanting to tranfer because I am going through a similiar situation with another card. I do not believe the actual credit transfer hurts you at all but you have to remember if it is a large amount you are transferring and do not have it paid in that intro period you will be charged back interest
Balance transfer is great if you have the funds to pay it down before the grace period, this is where a lot of people get stuck, end up with a huge transfer then a huge intrest rate a few months down the road when they can't afford to pay it off.
As fireyone stated, I don't think that balance transfer itself affects your credit, the huge balance would surely affect it, it lends to the debt/credit ratio on your report, which may be the same if you are transferring cards that are already being reported.
It can hurt yoru credit score depnding on from which account you are transfer the money from to which account
If you do a balance tarsnfer from a installment account to a credit card then yoru credit card utilization will show high and probably coudl lower the score
If you transfer from a credit card with high limt to a lower limit card it can lower yoru score
If the transfer is between simialr cards with the same limit that may nto have any impact
But rememebr that, probaly the credit card compnay may do a soft check on your credit report before approving your balance transfer. that may drop the score by few points