Which Steam badges can be currently obtained without any game cards?
By looking here and here you can see that the non game dependent are:
- The Community Leader badge
- The, so far, 15 Years of Service badges
- And the Gem badge
Plus some other ones that are impossible to get because they are either only earn-able during a limited time, or are for valve employees, translators or mods.
I got 100+ Badge - Power Player, After I bought 100 games on steam.