If you happen to have a small dog that can travel inside the cabin with you, or you are wealthy enough that your dog travels with you inside a private plane, then I'd say go for it, as you'll be right there to provide your pet comfort. However, for many mid-sized to large dogs, they are relegated to the unpleasant cargo area where the noise of the engines are amplified, they aren't allowed to leave their cramped cages to relieve themselves (no matter how long the flight is), and they don't have access to fresh food and water.
The cargo area is also subject to extreme temperature swings, ranging from very cold to very hot, depending on where you depart from and where you land, and there will be no one there to make sure your pet is managing those conditions comfortably. Moreover, your pet will have no idea what's going on and will likely panic, especially with the onslaught of unfamiliar smells and sounds. Some people say sedating your pet will do the trick, but I've never been comfortable doing that, and drugging an animal can also lead to other problems.
A simple search online shows that many people's beloved pets have died on flights due to extreme conditions or improper handling. Such as this, or this and this. Pets have even been lost.
As much as I love my pet, if I had to fly somewhere for some reason and the only way he could come with me was via flying in cargo, I would dismiss the idea immediately and find a caretaker for him instead. If I had to move somewhere, then I would find him a good home with a family who would care for him and love him. He may always wonder where I went, but I would rather experience heartbreak and let him wonder than let him suffer even one moment on a plane; not to mention the lengthy and harsh quarantine conditions that many governments impose on animals when you move to their countries with a pet.
I have come across several airlines that cater especially to animals, each one claiming that they will handle your pet in only the most humane fashion, such as Air Animal and Pet Shipping. I have never tried any of these services though. Have you? Leave a comment below with your experience.