Raikou can be found on Route 45 in the Johto region only after defeating the Elite 4.

If you accidentally defeat Raikou, he will respawn in 7 days.  Once you capture Raikou, he will no longer respawn.

You can also receive an Raikou Egg as an Ultra Rare drop from defeating the Legendary Dogs Boss on Four Island.

How to get to Raikou

Image from PokeoneCommunity.com and updated.

1) Fly to Blackthorn City.

2) Go South to Route 45 and go to the southeast corner.

3) You will run into Eusine in this area and he will want you to gather 25 crystals, which you get by defeating wild Pokemon in the surrounding area.

4) After gathering the questions, talk to Eusine, then talk to the rock in the crater and Raikou will appear.