Best overall local experiences search
There are hundreds of companies offering local activities and tours all across the world. PlacePass searches the biggest ones, including Viator and GetYourGuide, all at once for you. They offer over 100,000 experiences in 800 destinations and growing. While still a relatively new company, their website is well designed and the large amount of results for each city bear out its claim. At the least it's a great place to start your search.
Great for booking discounted local experiences and services in Asia
Klook is a must check for anyone traveling to Asia and Australia. They curate a great selection of must do local activities, many with exclusive discounts they've negotiated. Convenient services like airport pickup and wifi hotspots are also listed. We've booked these additional services ourselves and can attest to their usefulness as organizing them separately can be a pain. Their website and apps are clean and easy to use.
They've begun expanding to North America and Europe but it's still relatively sparse there. Expect that to improve over the coming year.
For more in depth, intellectual tours
If you're well traveled and crave more insight into a locale than the typical free walking tour, try Context Travel. They set themselves apart by hiring Ph.D and MA level scholars to lead tours that provide deep, intellectual insight for culturally rich cities across the world. We joined one explaining the intricacies of Japanese zen gardens in Kyoto and it was magnificent. They're typically a bit more expensive than other tours, but considering the quality and how different they are we think they're worth it.
For private or customized tours led by locals
No one's going to know a place better than locals, at least according to ToursByLocals. It's a marketplace that connects travelers with local guides, vets the guides to ensure quality, and takes care of the payments to ensure guides deliver on what they promise. These locals do post their own tours, but what's even better is they make it easy to contact these guides directly to set up custom private tours that cater directly to your interests and needs. No cookie cutter tours here. They should just default the tours to "Places to take pictures that'll get the most likes."
For hip and atypical experiences
Airbnb's recent foray into local experiences is still growing, but what they have so far is promising. As the resident "hip" brand among modern travelers, their experiences tend towards the opposite direction of the tourist laden "must dos" you see on TripAdvisor. Think socially conscious produce gardening, cave diving, electronic music production classes, etc all lead by local experts. The branding for each class is beautifully done and it's all built using Airbnb's signature design. If Airbnb lists experiences for where you're traveling to, it's worth checking out.