bitcoins can use different algorithm, how and implications
The only way to do this would be to announce a new version of the protocol well in advance. It would need to co-exist in the same blockchain with the existing keys and transactions and be adopted over time.


First, the client software with support for the new scheme needs to see widespread adoption before anyone can use the new algorithm
Once that has happened, early adopters (probably mining pools) can start creating keys in the new format and the blockchain will accept them.
If that worked well, the standard client will default to making new keys
Some more time down the road, everyone can agree that transactions can only be done to new keys, forcing the "old money" out of the system eventually



  Bitcoin could in theory switch to use the SCrypt Litecoin algorithm. (hence there is no reason for Litecoin to exist) 


I don't think that would be a good move. If people decided that the Litecoin algorithm is better, they can just use Litecoin. Bitcoin should stick with its algorithm, but make adjustments to parameters such as key length when those become necessary.

Choice of algorithm should be choice of blockchain (Bitcoin vs Litecoin) and can be left to the "market" to decide.