My newest article is now on GameDevTuts! It’s called 9 Rare and Underused Game Genres Ready to Explore.
Even Payday, which is a shooter, offers tons of non-violent ways to complete missions, which often are more tense and interesting than just having to shoot enemies.
Focus the gameplay on avoiding guards and staying in the shadows. Alarm systems and lasers offer puzzles to work around. Loot strewn around the level, with various risks attached to it, offer meaningful decisions: do you risk the reward, or do you play it safe?
Payday 2 is wonderfully designed in that it actively fosters greed. You only get a payout if at least one person makes it out alive, but every person left behind carries also a penalty. If somebody is downed, your first instinct would be to save them, but that would risk the entire enterprise, and thus the reward.