Also, I've known PHP to pass mail to sendmail but sendmail doesn't actually send it due to the 4pth parameter being missing in the call to mail().
@jarv what this means is that you need to set an additional 'from' field in the 4th parameter. PHP.net will show you how to do this.
As the others have said though, you also need to check your logs if you have access (not everyone does) and any spam folders etc.
My helpful sig is on vacation trying to loose some weight. It got a bit fat and caused a few problems but it will be back at some point!