It depends on how you declare it. You should read the documentation on memory management. Basically the rules are:
NSString *aString = [NSString stringWithString:@"Hello"];
NSString *bString = [NSString stringWithFormat:@"%@", @"Hello"];
In these cases, the string is not copied or retained. It is autoreleased, which means it will be automatically deallocated the next time the autorelease pool drains. You do not have to call the release method on them. (So assigning a new value will not cause it to leak.)
NSString *cString = [[NSString alloc] initWithFormat:@"%@", @"Hello"];
[cString release];
According to Objective C convention, methods that use alloc and have a retain count of one are not autoreleased, so you need to release them explicitly. Assigning a new value without releasing the old one will cause a leak.
You can also explicitly call a "copy" method or a "retain" method on a string. In either case, the new string will have a retain count of 1 and will not be autoreleased, so you will need to call the release method on it before you assign a new value.
NSString *dString = [cString retain];
NSString *eString = [cString copy];
...
[dString release];
[eString release];
If it is a property, and you use self.variableName, this will be taken care of for you (through the getters and setters which are generated with @synthesize). If you do it explicitly, you must make sure to call release on variables that you have called retain or copy on.
Edit: As some commentators below have noted, thinking about management in terms of "ownership" is usually the preferred of describing these ideas, rather than retain count.