Do transfering steam games to another computer reset that game's save data?

If you have Steam Cloud synchronization enabled, any applicable games will back up their saves to the cloud so you can access them from whatever device you install the game on.

To make sure this option is turned on:

1. Open Steam
2. In the top right, click Steam, then click Settings.
3. Click Cloud on the left hand list.
4. Make sure Enable Steam Cloud synchronization for applications which support it is checked.

You should be good to go after this! Note that some games might not be compatible with Steam's cloud support, but most modern games should be.

Some games use the Steam cloud sync as Kaizerwolf wrote, some don't

In addition enabling Steam Cloud Sync, you could potentially copy over most of them yourself.

A lot of games store their saves under

C:\Users\<Username>\Documents\My Games

If you copy this entire directory over (or individually for saves that you're missing), you'll be able to ensure most of your saves are moved across.