I'm always surprised at how many drummers I see carrying their drums around with no cases. I'm not just talking about cheap, entry level kits either.  I recall one concert date where the opening act's drummer showed up with a beautiful, top-of-the-line Gretsch drumset... and no cases!  When I asked him why he was carrying this great instrument around with no protection, he gave the answer I usually get, "I can't afford cases."  If you have spent hundreds or thousands of dollars on a set of drums, you can't afford not to have cases.  Heck, cardboard boxes would be better than nothing!!

For drummers on a budget who can't afford heavy duty road cases available from companies like Anvil, or even the molded plastic cases available from companies like SKB, you can buy a set of relatively inexpensive, unlined fiber cases - I recommend Humes & Berg - and by putting in a little work, make them last a long time while providing superior protection for your drums.

Treating the exterior of the cases: If you do nothing else, DO THIS.

Get some clear polyurethane varnish (oil based) and apply 1 or 2 coats to the outside of the cases.  This will toughen them up, waterproof them, and greatly extend their life.

Inside protection:

Padding the inside of the cases is highly recommended, especially if you are carrying your drums around a lot.  Most companies that sell fiber cases offer foam-lined cases as a (more expensive) option.  The problem with buying foam-lined cases is that as the years go by and the case is repeatedly packed and unpacked, the foam will start wearing away and breaking down, sometimes leaving sticky residue on the drums. To replace the lining the old foam has to be scraped away, which is messy and time consuming.

Here are a few inexpensive and effective methods to pad the inside of the cases and further protect your drums.

Good - Buy some old bath towels from thrift stores, garage sales, etc.  Wrap each drum in a towel before stowing it in the case.

Better - Scrounge up pieces of scrap foam and simply pack them around the drums.  When a piece of foam starts to wear out, throw it away and scrounge up some more.

Best - Procure some quarter inch thick, dense foam (I recently bought a 4' X 10' sheet - enough to line several cases - for about $20), cut it to fit and line the inside of the cases using contact cement to hold the foam in place.  Glue only the top and bottom edges so when the foam does wear out, it can be replaced without having to scrape away a lot of gunk.

A lot of the drums I've owned have been carried around in fiber cases that have been "modified" using the above methods.  They have traveled in cars, trucks, vans, buses and airliner baggage compartments where they have been stacked, packed, dropped, thrown, rained on and generally abused.  Some of these cases are over 20 years old.

I have never had a drum damaged during transport...