For sure:
Yandex.Metro
St. Petersburg's excellent subway (metro) system, in addition to being exquisitely beautiful, is often the fastest way to get around the city. The trick is knowing which lines to take and when to switch between them. Yandex's brilliantly simple Metro app (App Store; Google Play) will find the best route, tell you how long it'll take you to get there, and even tell you how many trips you've got left on your pass.
Yandex.Taxi
If the metro isn't your thing, you can also get around the city in style in comfort using a taxi. Yandex recently bought out Uber in Russia, so the Uber app installed elsewhere won't work; you'll be prompted to download Uber Russia, or you can go straight to the source and get Yandex.Taxi (App Store; Google Play)
Visit-Petersburg
The city’s official app is more or less what you’d expect: it offers you the basic info on sights and landmarks, helps plan routes, browse restaurant reviews, find events, and has a handy currency converter. Another neat future are the free audio guides to the city.
The Russian Museum apps
The Russian Museum is collaborating with the global audio-guide platform izi.TRAVEL on a range of guides to the museum. It has an offline mode and, yes, it does have in-app purchases. The full list of the museum's apps includes some fun free apps, such as the Treasures of the Castle quest and a guide to the Summer Garden.
Maybe:
PaperApp
Recently launched by the popular media portal Paperpaper, this app (App Store) is akin to a crowdsourced map of the city featuring comments from the editorial team and other users. It works best if you want to see the city through locals' eyes, and if you like sharing your impressions with others. More of a social experience than a straightforward guide, it's sure to help you find some authentic adventures.
Meh:
State Hermitage Museum
Surprisingly, the State Hermitage Museum's app seems to be more about in-app purchases than actual quality of content. Save your money.
Wonder what we're addicted to? Here's some apps we love here at ITMO.