I've tried lots of different things:
FedEx Ground
Shipped an F tuba in an Anvil flight/shipping trunk cross-country (to myself, actually) without any problems. I made all the arrangements online and arranged and had it picked up by FedEx the next day without any problems. Cost wasn't unreasonable, but totally depends on size, weight and where the package is coming from and going to. Depending on the location of the recipient, FedEx could be one of your only options, as they seem to go just about everywhere.
Overall: No problems.
UPS Ground
Shipped the above mentioned F tuba in the same Anvil case that had gone through shipping and air travel (with no problems). The recipient discovered that the top bow of the tuba was partially crushed in transit. I had made the shipment from a real UPS drop of location (mostly for air cargo), not one of those mailboxes/pack-n-ship type places, and had insurance on it. I made an insurance claim on the damage, UPS "investigated," and I ended up with a check from them that covered all of my shipping expenses (including return shipping to me) and full repair costs to restore it to former glory.
I used them again several years later to ship a tuba inside a gig bag and inside of an Anvil trunk. Did the arrangements online, had it picked up and shipped with no questions asked. That time, no problems whatsoever.
Overall: 1 good, 1 bad. Paid on insurance claim (though I wouldn't count on this always being the case).
DHL Trucking
Shipped a MW in an aluminum flight trunk. Case got a little banged up (as you might expect), but no serious damage to case and none to the tuba. I'm not really sure if that's a testament to the MW case or the way DHL ships things though...
I also received a tuba this way (packed in huge cardboard box) without incident.
DHL was pretty cheap when shipping, too (c. $30 something dollars, as I recall).
Overall: No real problems. Case getting banged up was inevitable.
Greyhound
Shipped a big CC tuba from Texas to far northern Michigan via Greyhound (at buyers request). Package service on Greyhound is cheap, but they don't provide service everywhere like FedEx or UPS does. Greyhound also offers no tracking service and very little insurance coverage. It might also be worth mentioning that with Greyhound your tuba is never more than a foot or so off the ground. That doesn't make it damage proof, but it sure helps.
I recently received an empty tuba case shipped via Greyhound. No issues and transit time from New York to Indiana was under 10 days, as I recall.
Overall: No problems in two uses.
Amtrak
I've sent and received tubas via Amtrak. It has always been under $50, fast, and reliable, and incident free for me. In addition, they let you (or at least did) buy insurance in whatever amount you want. The kicker is that you have to live somewhere that Amtrak provides their package express service. They don't do it for all of their stops. Their paper work also serves as a way to track the shipment.
Overall: No problems. My personal favorite.
Things I've learned:
-Nobody really cares about your stuff. They will throw it, stack stuff on it, drop it, leave it unattended, set it down in a puddle, etc.
Be prepared for that.
-Don't ship a tuba in a case. I've had mixed results with this. My UPS shipments were with custom form fit Anvil cases, which are a lot beefier than the cases most people use and I still got damage. On the other hand, the big CC I shipped via Greyhound went in a regular wood case (though the horn was tightly packed inside) without any problems. I consider myself lucky when it came to shipping in cases and wouldn't ship that way again.
I think the biggest problem with shipping is that the shipper doesn't pack the tuba up very well for the type of handling it will be subjected to. When I received a $1x,xxx tuba from Baltimore Brass (since sold) it came in a huge box full of packing peanuts and bubble wrap and held together with large brass staples that could have probably fit 3 tubas inside. They don't ship that way for fun, folks. No damage.
Trying to sneak through by shipping a tuba in a typical hard case or in a really-too-small box without enough wall clearance is just asking for it. Go back and read about the damage I got using ANVIL cases! Most damage that is shown and discussed on tubenet seems to happen because the horn does not fit will in the packing, usually a case. If the horn can move at all in any direction in the case, especially at the bell end, you're very likely to end up with damage. Most bell crunches and wrinkles happen because the bell slammed into the end or the sides of the case or box. It doesn't matter if your tuba is on a plane, train, or automobile...if it's packed poorly, it will likely end up damaged. Most (not all) well packed tubas will end up being too large to go FedEx, UPS, or USPS. Pack your tubas how they need to be packed...ship them by whatever means you have to in order to move a package that big. You'll probably discover that your typical "consumer" shippers aren't the best option.