It'd be an interesting thing to make FileReader conform to <NSFastEnumeration>, so you could do:

FileReader *r = [[FileReader alloc] initWithFilePath:pathToFile];
for (NSString *line in r) {
  NSLog(@"line: %@", line);
}
[r release];

The use and meaning of local variables in FileReader readline and readLineBackwards are not consistent. Especially, the character position at which the reader sits after one while loop in readLineBackwards is another then it is in readLine. That makes it difficult to use the class without knowledge about the inner semantics.
Further, readLineBackwards can be simplified by getting rid of the redundant if-clauses used before and within the while loop. That needs some brain power of course :-}

Stackoverflow code seems to be governed by this license:

http://creativecommons.org/licenses/by-sa/2.5/

I assume this codebase is therefore governed by the same license? At the moment, the code just says copyright/all rights reserved.

So you have a textfile such as:

diner
restaurant
lunch-spot
greasy spoon
café // "é" character
coffee shop
cafeteria

LineReader stops reading when it hits the "café" line above. Never gets to "coffee shop".

While it uglifies the code, it is best practice to prefix both class names and any category methods with some uniquish characters. JJD would be appropriate. Without namespaces in Cocoa, this provides a level of protection against collision if another set of source code. or a library or framework, also defines a similar thing called FileReader or implements a similarly named category method on NSData.

Cocoa will happily pick one, and it might not be the one you want, even if you omit the header files for colliding names.