Pokémon Red and Blue/Vermilion City

Do some Pokémon Trading
The trader won't deal with Yellow players, but they can talk to the girl just outside for a free once they've won the Thunder Badge. She is hoping that you will take good care of it.

Red/Blue players can trade a for a very rare  in the building above and to the right of the gym. Don't hesitate to make this great trade if you picked up the fairly common Spearow! If you don't have a Spearow to spare, you'll get a chance to grab one in the upcoming Route 11

Many important items
Convince the old man in the building left of the Pokémon Center that you love fishing as much as he does and he'll take a shine to you. He will give you his Old Rod as a gift! Now you can use it near any body of water and get... a. Or... another Magikarp. Yes, that's all this Rod catches. Good news if you didn't buy one earlier.

Something slightly cooler than the Magikarp Stick can be found at the Pokémon Fan Club, located directly above the gym. Listen to the president's boring story and he'll give you his Bike Voucher. Redeem it at the Bike Shop in Cerulean City, and you'll get a Bicycle you can use anywhere!

Trainer Battle 3: Lt. SURGE
Use cut to hack down a bush and reach the Vermilion City Gym entrance. Once inside, you'll be confronted with a few trainers and a double-locked door. To reach Lt. Surge, you'll have to find the two switched hidden in the cans on the floor. The switches are randomly located, but once you find one, the second will be right next to it. If you don't get it on your first try, the switches will move and you'll have to search again.

As for Surge, his powerful is certainly a dangerous opponent, but strong Ground-type Pokémon like  and  are completely immune to many of his attacks, and your own Electric and Grass Pokémon have some protection. On offense, use your own Ground-type attack, Dig, for devastating results. With any luck, you caught a Geodude or two back at Mt. Moon. If you didn't, make a detour down nearby Route #11 into Diglett's Cave. There you can capture some and  to even out the odds with Lt. Surge. Otherwise, stick with normal attacks.

Your prizes include the Thunder Badge and TM 24, which can teach the powerful electric attack Thunderbolt to a variety of Pokémon. This includes Pikachu, but in the Yellow version, he'll learn it by himself at level 26, so you may want to use it on someone else, or save it for or another Electric Pokémon.