What is the appropriate ratio of Medics to team size for most non-pro games? I'm fairly sure one medic in twelve players isn't effective.
A straight ratio isn't the best, because there are some classes that the medic doesn't synergize well with (engineer, spy). A better metric would be 1 medic for every 4-5 offensive classes, so 2-3 medics on a 12 person team.
There's not a set ratio, but they key is to at least have 2 because medics are exponentially better when they can heal each other. 1 medic is bad not because they can't heal as many targets (though of course that's bad), but because when they get hurt, they have to back off the line to heal themselves.
I'll add one more answer: it depends on what stage of the game you're in and what mode you're playing. In Attack/Defense, if you're on BLU, it's very helpful to have more medics than usual at the beginning of the round (as long as each of them has an offensive player to buddy up with) because they can all build up an Ubercharge before the round starts. Then when the gates open they can Ubercharge more than one offensive class player at the beginning, or extend an Uber started by another Medic on a Heavy or Pyro (which is what I usually do, RED is usually ready for Ubers out of the gate with their own Uber but they don't expect yours to last twice as long). I'll often start a round as a medic and then switch to another class after that first uber is spent, assuming there's another medic on my team.
In CTF, the Quick Fix is handy for buddying up with Scouts, since it speeds up the Medic to the Scout's speed and its super-healing Ubercharge doesn't prevent the Scout from grabbing the intelligence (which the normal Medi-gun uber does).
If you're playing with a team of 12 people and someone else has your role, then become a medic and support him. My ratio would be 5-1 or 4-1 depending what class they are.
It's very tough to give a hard-and-fast rule about this, since it varies by map and game type, and also depends on what classes / tactics the enemy team is using, as well as what classes your teammates are already playing. It also depends on how many medics the other team has.
Generally speaking the team with more medics will win, as long as there are ample "offensive class" players to heal. Generally Heavy, Soldier, Demoman, and Pyro are the classes that pair well with medics.
If you have one medic on a 12 player team, and the other team has zero, you'll probably win faster if you go for one of the powerful attacking classes than if you decided to switch two players to medic.
For example, if the enemy team has decided to turtle with a lot of sentries, and your team is full of scouts, snipers, engineers, and spies, you probably will help out a lot more by switching to Demoman or Soldier to counter the sentry positions than you would by trying to heal those other classes as a medic.
I usually switch to medic if one heavy is present and no medic support him. I would say 1 medic foe 2 heavys.
On the other hand, like Raven Dreamer said, 1 medic for 4-5 offensive players is nice.
At least 1 per every 5 players, with 3 of them being offensive is usually what we roll with.