Number of occurrences of a substring in an NSString?

This isn't tested, but should be a good start.

NSUInteger count = 0, length = [str length];
NSRange range = NSMakeRange(0, length); 
while(range.location != NSNotFound)
{
  range = [str rangeOfString: @"cake" options:0 range:range];
  if(range.location != NSNotFound)
  {
    range = NSMakeRange(range.location + range.length, length - (range.location + range.length));
    count++; 
  }
}

There are a couple ways you could do it. You could iteratively call rangeOfString:options:range:, or you could do something like:

NSArray * portions = [aString componentsSeparatedByString:@"cake"];
NSUInteger cakeCount = [portions count] - 1;

EDIT I was thinking about this question again and I wrote a linear-time algorithm to do the searching (linear to the length of the haystack string):

+ (NSUInteger) numberOfOccurrencesOfString:(NSString *)needle inString:(NSString *)haystack {
    const char * rawNeedle = [needle UTF8String];
    NSUInteger needleLength = strlen(rawNeedle);

    const char * rawHaystack = [haystack UTF8String];
    NSUInteger haystackLength = strlen(rawHaystack);

    NSUInteger needleCount = 0;
    NSUInteger needleIndex = 0;
    for (NSUInteger index = 0; index < haystackLength; ++index) {
        const char thisCharacter = rawHaystack[index];
        if (thisCharacter != rawNeedle[needleIndex]) {
            needleIndex = 0; //they don't match; reset the needle index
        }

        //resetting the needle might be the beginning of another match
        if (thisCharacter == rawNeedle[needleIndex]) {
            needleIndex++; //char match
            if (needleIndex >= needleLength) {
                needleCount++; //we completed finding the needle
                needleIndex = 0;
            }
        }
    }

    return needleCount;
}

Here is a version done as an extension to NSString (same idea as Matthew Flaschen's answer):

@interface NSString (my_substr_search)
- (unsigned) countOccurencesOf: (NSString *)subString;
@end
@implementation NSString (my_substring_search)
- (unsigned) countOccurencesOf: (NSString *)subString {
    unsigned count = 0;
    unsigned myLength = [self length];
    NSRange uncheckedRange = NSMakeRange(0, myLength);
    for(;;) {
        NSRange foundAtRange = [self rangeOfString:subString
                                           options:0
                                             range:uncheckedRange];
        if (foundAtRange.location == NSNotFound) return count;
        unsigned newLocation = NSMaxRange(foundAtRange); 
        uncheckedRange = NSMakeRange(newLocation, myLength-newLocation);
        count++;
    }
}
@end
<somewhere> {
    NSString *haystack = @"Cheesecake, apple cake, and cherry pie";
    NSString *needle = @"cake";
    unsigned count = [haystack countOccurencesOf: needle];
    NSLog(@"found %u time%@", count, count == 1 ? @"" : @"s");
}

If you want to count words, not just substrings, then use CFStringTokenizer.

Matthew Flaschen's answer was a good start for me. Here is what I ended up using in the form of a method. I took a slightly different approach to the loop. This has been tested with empty strings passed to stringToCount and text and with the stringToCount occurring as the first and/or last characters in text.

I use this method regularly to count paragraphs in the passed text (ie. stringToCount = @"\r").

Hope this of use to someone.

    - (int)countString:(NSString *)stringToCount inText:(NSString *)text{
        int foundCount=0;
        NSRange range = NSMakeRange(0, text.length);
        range = [text rangeOfString:stringToCount options:NSCaseInsensitiveSearch range:range locale:nil];
        while (range.location != NSNotFound) {
            foundCount++;
            range = NSMakeRange(range.location+range.length, text.length-(range.location+range.length));
            range = [text rangeOfString:stringToCount options:NSCaseInsensitiveSearch range:range locale:nil];
        }

        return foundCount;
   }

Example call assuming the method is in a class named myHelperClass...

int foundCount = [myHelperClass countString:@"n" inText:@"Now is the time for all good men to come to the aid of their country"];

No built-in method. I'd suggest returning a c-string and using a common c-string style algorithm for substring counting... if you really need this to be fast.

If you want to stay in Objective C, this link might help. It describes the basic substring search for NSString. If you work with the ranges, adjust and count, then you'll have a "pure" Objective C solution... albeit, slow.