you can also play tails doll. (you need a password, which is something you can figure out yourself)
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Yes. Just go 2 options, and select the character you want to play as: Sonic, Tails, or Sonic and Tails. NOTE: If you are just as Tails, you cannot go SUPER SONIC, however there is a cheat to go SUPER TAILS, but you need both Sonic and Tails to do this.
In the real game no, because Tails wasn't introduced until Sonic 2. You can however use hacks people have created to play as Tails in Sonic 1. Try out this one on Sonic Retro, that allows you to do just that
play can you feel the sunshine 1 hour loop at 3:00 AM
Sadly, no. Tails is not playable. He does however have a massive role in the game, and is in almost every cutscene with Sonic.
You could play it on both. Any DS game can play on your DSi