I guess you're referring to downloaded music, which does have that limit (three devices max for downloaded content). You can see your offline devices here.
About playlists that are not downloaded - no limits here! You can access your playlists on as many devices as you possibly need. :) All you'll need is an Internet connection to let Spotify load your playlists up from the servers. Online playlists are not device-specific.
Hope that helps! :)
SebastyRock Star 16
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