I have travelled on Continental, Delta and American carriers with both rifles and handguns, no great problem as long as the weapons are secured in FAA approved cases and locked, an FAA security tag declaring the weapons are 'unloaded' is manditory and signed. The tag is to be placed inside the case, do not let any inexperienced agent at the check in desk put it on the outside of the bag. Ammunition to be store in again an FAA approved carton (plastic ammo box will do, I put a bit of tape over the lid). FAA maximum weight for ammunition is 5 kilos.
European carriers are similar but obviously will want to check the international paperwork, and they will fax ahead.
You will be required to accompany the baggage to the security area whilst the TSA people turn your stuff upside down. They examine everything and tape the ammo boxes back up with their security tape.
A word of caution these guys are not too bright, and extremely clumsey. They will not make good any damage to equipment or baggage caused during the search, make sure they have the right keys, because they will not think twice or wait for you to find the right keys.
Example I had taken a rifle stock over to some pals of mine in Ft. Worth, and they refinished the stock, no metalwork, just the wood. To protect it I had wrapped it in bubble rap, they sliced it open with a knife (slashed is nearer the mark), the stock and finish was badly cut up......
Hope this was helpful..................................