SAN FRANCISCO—The social calendar posted on a wall at Internet start-up Airbnb Inc. is covered in multicolored sticky notes. A recent Wednesday was blocked out for a wine and cheese mixer and an all-hands talk on stock options. Friday brought a rooftop barbecue, and Saturday there was an air-guitar contest.

Then there are the regularly scheduled perks at the 120-person vacation-rental marketplace outfit, including Mustache Mondays (employees wear fake ones), Yoga Tuesdays (before company lunch) and Thursday Recess (company-wide...