You should use NSIntegers if you need to compare them against constant values such as NSNotFound or NSIntegerMax, as these values will differ on 32-bit and 64-bit systems, so index values, counts and the like: use NSInteger or NSUInteger.
It doesn't hurt to use NSInteger in most circumstances, excepting that it takes up twice as much memory. The memory impact is very small, but if you have a huge amount of numbers floating around at any one time, it might make a difference to use ints.
If you DO use NSInteger or NSUInteger, you will want to cast them into long integers or unsigned long integers when using format strings, as new Xcode feature returns a warning if you try and log out an NSInteger as if it had a known length. You should similarly be careful when sending them to variables or arguments that are typed as ints, since you may lose some precision in the process.
On the whole, if you're not expecting to have hundreds of thousands of them in memory at once, it's easier to use NSInteger than constantly worry about the difference between the two.