In Pokémon HeartGold & SoulSilver, you will find that your rival isn't a buddy or a friendly childhood rival like in the past games. Instead, this time, your rival is a dark, sinister character. He starts off by stealing a Pokémon and continues on the dark path until you gradually show him the error of this ways. This page details all of your encounters with him. Unlike past rivals, his team doesn't change depending on his starter Pokémon

Cherrygrove City After you have obtained the Pokédex from Professor Oak in Route 30 and return back towards New Bark Town after a call from Professor Elm stating he has been robbed, you will encounter your Rival as you exit Cherrygrove City. He will quickly challenge you so that he can get past Passing Boy Chikorita/Cyndaquil/Totodile Lv. 5
Sprout Tower When you reach the top of the Sprout Tower, you will encounter your rival again. Here, he will have just defeated the Monk and earned Flash. He will quickly spot you and then instead of challenging you, he will use an Escape Rope to exit the Sprout Tower.
Azalea Town Your next encounter with your rival will be when you are in Azalea Town. If you go west towards Ilex Forest, he will come up to you and challenge you yet again. He will vow to defeat you and defeat all weak trainers as well as Team Rocket. Defeat him, and he'll let you pass into Ilex Forest Rival Silver Gastly Lv. 14 Zubat Lv. 16 Bayleef/Quilava/Croconaw Lv. 18
Burned Tower The next encounter is another battle. You will find him in the Burned Tower with Morty & Eusine where he will be looking for the Legendary Pokémon so he can further defeat the weak trainers. Once he spots you, he will challenge you again Rival Silver Gastly Lv. 20 Zubat Lv. 20 Magnemite Lv. 18 Bayleef/Quilava/Croconaw Lv. 22
Olivine City When you first enter Olivine City, you will walk past the gym. Once you do, your rival will come outside from the gym and inform you that the Gym Leader, Jasmine, isn't at the gym, but is at the lighthouse taking care of an ill Pokémon. He will comment that the Pokémon is useless and then leave.
Mahogany - Rocket Hideout When you've fought your way to the end of the Mahogany Rocket Hideout, your Rival will appear again. Here he says that he will stop Team Rocket himself but mentions he bumped into Lance who criticised him for the way he treats Pokémon. He will say you're not strong enough to defeat Team Rocket and then leave again
Goldenrod Radio Tower In the Radio Tower, you will find your rival again. After you have donned your Team Rocket disguise to enter the Radio Tower, your rival will quickly come and blow your cover. He will expose you for not being a Team Rocket member and then quickly leave again, leaving you to deal with Team Rocket yourself.
Goldenrod Underground In the Goldenrod Underground, you will once again meet up with your rival. He will again challenge you for being weak, and once again challenge you to a battle. Once defeated, he will start to question whether Lance is right and leave to begin training properly. Rival Silver Haunter Lv. 32 Golbat Lv. 32 Magnemite Lv. 30 Sneasel Lv. 34 Meganium/Quilava/Feraligatr Lv. 34
Victory Road At the end of Victory Road, you will encounter your rival once again. He will say he has been training and intends to challenge you once again to show that he is the stronger trainer Rival Silver Sneasel Lv. 36 Golbat Lv. 38 Magneton Lv. 37 Kadabra Lv. 37 Haunter Lv. 37 Meganium/Typhlosion/Feraligatr Lv. 40
Mt. Moon Your next encounter with your rival will be while he is off training in Kanto. When you first enter Mt. Moon, he will spot you and tell you that he has been training to become a better trainer and once again, requests a battle with you Rival Silver Sneasel Lv. 46 Golbat Lv. 47 Magneton Lv. 46 Alakazam Lv. 48 Gengar Lv. 48 Meganium/Typhlosion/Feraligatr Lv. 50
Dragon's Den Your next encounter with your rival will have you meet him in the Dragon's Den. Here, he is training his starter when Clair & Lance both appear. They see both of your skills and challenge you to a Double Match. This teamwork shows that your rival is now able to care for his Pokémon You & Your Rival Clair & Lance Dragonair Lv. 52 Kingdra Lv. 56 Dragonite Lv. 60 Meganium/Typhlosion/Feraligatr Lv. 60 Crobat Lv. 58 Gengar Lv. 56 Gyarados Lv. 68 Charizard Lv. 68 Dragonite Lv. 75
Dragon's Den After this, on Tuesdays & Thursdays, you will find your rival is back in training in the Dragon's Den. Here, he is not battleable but will talk to you about him realising that he was wrong at the get-go and you should not treat Pokémon as tools.
Pokémon League On Mondays & Wednesdays however, when you enter the Pokémon League, you will get challenged by your rival before you enter. He has been training and wants to test his team out Rival Silver Crobat Lv. 58 Magneton Lv. 55 Gengar Lv. 58 Sneasel Lv. 55 Alakazam Lv. 56 Meganium/Typhlosion/Feraligatr Lv. 60
Three Years Ago... During the special Celebi Event, where you take a special Celebi to Ilex Shrine, you will be sent back in time three years where you will see Silver and his father fighting in Route 22. This is where you will see why he has a great dislike for Team Rocket and why he turned bad at the outset.