Yes , it can be done .
ex :
Code
mysql> ALTER DATABASE xxx DEFAULT CHARACTER SET UTF8 COLLATE UTF8;
There are also commands to change TABLE/COLUMN's collation . But it only affects the newly inserted data , not the existing data.

English is not my native language. I try my best to express my thought precisely. I hope you understand what I mean. If any misunderstanding results from culture gaps, I apologize first.