The app is very good, and is certain to drive people to iTunes as their music and movie organizing software. I'm kind of surprised that Apple waited this long, particularly as it's very similar to what Signal and Remote Buddy have been delivering for a year.
If you have an iPod Touch, you can still use Remote. You have to buy the iPhone 2.0 software version for Touch. Just go to apple.com (or your national suffix) to go through the motions. Costs 9.99 US (big surprise.)
You can then "buy" Remote from the AppStore - it's free, but it's the same process. You can also use most of the other app's now available on your Touch.
I used Remote Buddy because there wasn't an alternative, but so far Apple's native solution seems faster, and has all the features I need. It also seems to be kinder on the battery. which is always a good thing.
The next thing I want is hardware control. There have been several solutions suggested, I have even seen a prototype that looked very promising. Yesterday, I noticed something called IControl (I-love-control) available through the AppStore, but they want to send an installer home to me, and that shouldn't be necessary.
Note that Remote hasn't been released to all markets yet, but should be shortly.