Hi there, since I didn't see anything on the subject I thought I would create a topic to let people be aware of these cool unlockables.
Similar to Pokemon Diamond, Pearl, and Platinum Versions there is secret unlockable Wallpaper for your PC Box that is accessable in Pokemon HeartGold and SoulSilver Versions. In addition this time around, there are also three Pokemon Eggs that can be unlocked through this method.
To get started, first go to the Violet City Pokemon Center. Look up your five digit Trainer ID which can be found on your Trainer Card. Next, once you have your Trainer ID number go on over to Filb's Secret Phrase Generator which can be found here. Enter your Trainer ID number into the box, select the first game option (HeartGold or SoulSilver) and Select your game language (English Version is the Second option). Once done, click the button to get your phrases generated! Now back in the Violet City Pokemon Center, talk to the man to the right of the PC and tell him any of the phrases that are shown to unlock that Box Wallpaper or Pokemon Egg.
If you have the Japanese Version of Pokemon HeartGold or SoulSilver Version you can follow the same steps just choose Japanese Version as the language (which is the first option under language). All of the Japanese Secret Phrases have been revealed totaling up to 8 Box Wallpapers and 3 Pokemon Eggs.
As for the English version, only 2 Box Wallpapers have been revealed and 1 Pokemon Egg. Here are the ones that have been revealed:
Trio Box Wallpaper (Start)
Spiky Pika Wallpaper (Released March 25th, 2010)
Mareep Pokemon Egg (Revealed March 25th, 2010)
Heart (Released April 2nd, 2010)
Soul (Released April 9th, 2010)
Wooper Pokemon Egg (Revealed April 9, 2010)
Here are all of the Box Wallpaper and Pokemon Eggs, incase you are interested: