I haven't looked at any of the solutions. Or any of the other comments.So at the risk of posting a redundant comment :

Alice guesses that Bob's coin is the same as hers. Bob guesses that Alice's coin is the opposite to hers.

It's fairly straightforward. I'd like to know the computer science angle to this though.

EDIT: From the computer science that I know :

We need to find an invariant that all permutations of coin flips always satisify. Intuition tells us that Alice's coin might be the same as Bob or vice versa :

If you construct a truth table :

  Alice  Bob     Alice's Coin same as bob    Bob's opposite to Alice

  H      H               YES                            NO

  T      T               YES                            NO

  H      T               NO                             YES

  T      H               NO                             YES

The expression :

  Alice's coin same as Bob || Bob's opposite to Alice

Always evaluates to true. So Alice can guess her flip and Bob can guess the opposite.

But what if we had Alice , Bob and George and atleast one of them had to get the other two right ?

Is there a general pattern ?

  Alice Bob George
  H     H   H
  H     H   T
  H     T   H
  H     T   T
  T     H   H
  T     H   T
  T     T   H
  T     T   T

Will try and figure it out over dinner :D .