What makes one cellphone ringtone better than another? Answer: annoyingness. Ringtones annoy by either being bad songs or by being overly loud or by being audible to anyone who is not the recipient of the call.
What is the ideal ringtone? Answer: A ringtone which is clearly audible by you, but remains inaudible, or just background noise, to everyone else.
Are there any noises which YOU hear better than everyone else? Answer: if so, make those noises your ringtone! You can then set your volume lower, be less annoying, and still get the same ability to hear your phone ring.
What if I don't know of such a noise? Answer: The cocktail party effect points out that you can hear your own name at lower volumes than other people will hear your name. In a crowded party, everything is background noise except you instantly notice when someone says your name.
What is the point of this? Answer: Your cell phone ring tone should be someone saying "Hey <your name>". It's an almost perfect solution. It allows everyone to know who's cell phone is ringing, and it allows you to hear your own cell phone at volume levels that won't annoy others. It means that a lonely ringing cell phone embarrasses its owner, rather than being a deniable event. And finally, unless your name is actually IN the song Mambo No 5, it means that I'll never have to hear that ringtone ever again.