There are no requirements. Use as many or as few colours colours as you feel you need to give your art the look it needs.

Individual sprites and tiles often have differing numbers of colours.

What's important is that it all looks good when put together. This often means reusing some key colours between assets, or perhaps even using a small palette for the entire game.

There is no ideal number of colours, it all depends on the look you want for your game. There are great-looking games that use only a few colours and there are great-looking games that use dozens or hundreds of colours - it's all about making sure the colours you choose work together, and that you use them intelligently.

If you're looking for a unique look to your game, consider using a small palette with an unusual colour scheme, rather than a palette that has ramps for every hue. Of course, colours aren't the only way to make your game look unique. For example, Magical Starsign has a huge overall palette, but it has a recognizable visual style because of the use of large areas of solid, bright colours with styled edges. Final Fantasy VI was unique at its time, and remains recognizable today, for its heavy use of texture and detail with subdued, often cool hues. It's important to pick a look that suits the tone of your game and stick to it - if you make every area feel completely different, the players won't feel like they're playing a cohesive whole.