iPhone App: how to get app icon from app id?

(I composed this answer after 2 minutes of googling... It's just the matter of the correct keyword!)

This is possible using an undocumented documented API of the iTunes Store. It might change in the future, but it doesn't seem to have changed in the near past, so here you are...

NSString *idString = @"id389801252";

NSString *numericIDStr = [idString substringFromIndex:2]; // @"389801252"
NSString *urlStr = [NSString stringWithFormat:@"http://itunes.apple.com/lookup?id=%@", numericIDStr];
NSURL *url = [NSURL URLWithString:urlStr];
NSData *json = [NSData dataWithContentsOfURL:url];

NSDictionary *dict = [NSJSONSerialization JSONObjectWithData:json options:0 error:NULL];
NSArray *results = [dict objectForKey:@"results"];
NSDictionary *result = [results objectAtIndex:0];
NSString *imageUrlStr = [result objectForKey:@"artworkUrl100"]; // or 512, or 60

NSURL *artworkURL = [NSURL URLWithString:imageUrlStr];
NSData *imageData = [NSData dataWithContentsOfURL:artworkURL];
UIImage *artworkImage = [UIImage imageWithData:imageData];

Note that this performs two synchronous round-trips using the NSURL API, so you better wrap this in a backgorund thread for maximal user experience. Feed this program an ID string (idString in the code above) and in the end, artworkImage will contain a UIImage with the desired image.

Just for reference, you can use the app's bundle id too:

http://itunes.apple.com/lookup?bundleId=com.burbn.instagram