Having to deal with shipping almost daily, UPS gets it right about 99.9% of the time.
However, when they do foul up, they are the WORST as far as actually doing something about it. I had the most frustrating time back in 2000 when they delayed one box which we needed desparately in setting up for a trade show. We knew it was in the right city, but somehow made it to the wrong depot. All we could do was wait two days for maybe a delivery tomorrow.
I also had them once return a package saying we refused it. The thing is, at the time they said they refused it, nobody was in the mailroom. He didn't get there for another half hour or so.
I always use FedEx when it is critical. DHL seems to have a good track record lately. Well, actually, I haven't had to find out the hard way when either of them misroute something.