Free and trusted are two words that generally do not go together. However since the crypto markets are still new and many people want to become a part of it, we have some of these "freebies" to attract new registrations. DEX like others said, list coins as soon as tokens are unlocked and for free like etherdelta and forkdelta.

However if you are looking for trusted exchange and they list for free, you should not go for a CEX. They will all ask for some amount of listing fees. Often they are pretty big, which Binance suffered from a few months back, getting a backlash from userbases.