NSDate stores dates relative to a standard reference date. From the class docs:
"The sole primitive method of NSDate, timeIntervalSinceReferenceDate, provides the basis for all the other methods in the NSDate interface. This method returns a time value relative to an absolute reference date—the first instant of 1 January 2001, GMT."
NSDate does not itself have any concept of time zones. So the NSDateFormatter did the right thing: it converted a date which you told it had a GMT offset (by specifying a time zone), and gave you a "normalized" NSDate for that date.
If you want to see the date represented in the Europe/Budapest time zone, either use your existing date formatter (-stringFromDate:) or the appropriate NSDate description method (e.g. -descriptionWithCalendarFormat:timeZone:locale:).
P.S.- You don't need an alloc/init at all in your code as written. In non-ARC that would be a leak.
P.P.S.- Your date format is incorrect and giving nonsensical results. I've gone ahead and cleaned up your code as follows (tested under ARC):
NSString *dateString = @"2011-09-02 17:49:54";
NSDateFormatter *dateFormatter = [[NSDateFormatter alloc] init];
NSTimeZone *tz = [NSTimeZone timeZoneWithName:@"Europe/Budapest"];
[dateFormatter setDateFormat:@"yyyy-MM-dd HH:mm:ss"];
[dateFormatter setTimeZone:tz];
NSDate *date = [dateFormatter dateFromString:dateString];
NSLog(@"%@", [dateFormatter stringFromDate:date]);
NSLog(@"%@", [date descriptionWithCalendarFormat:nil timeZone:tz locale:nil]);
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