Can a tapped creature attack or block?
According to the rules, tapped creatures cannot attack or block.  The only time that it matters whether or not they are tapped is when they assign to attack or block.  This means:


If you tap the creature before combat and have a way to untap the creature again, still before combat (such as Thousand-Year Elixir), it will be able to attack or block (it only matters that it is untapped when you assign it to combat).
If you tap your opponent's creature before combat (such as with Trip Noose), that creature will be unable to attack unless they have some means to untap it.
If a creature has been assigned as an attacker or blocker and subsequently becomes tapped, it will still be in combat (so you can block with Orim, Samite Healer and then tap it to use it's ability after you have blocked and it will still be a blocking creature).  This is consistent with the fact that creatures normally tap when attacking.
Because creatures normally tap when attacking, you cannot both attack with a creature on your turn and block with it on your opponent's turn (exceptions: if the creature has vigilance or you have a way to untap it).


Also of note: Masako the Humorless.