How common is traveling by bus in the US? Do Americans use buses often for long-distance travel?

There is some nuance to this question. For starters, I know you asked about inter-city travel, but let's start with more local travel. This is where buses shine, as they're basically a way of cheaply and easily bolting a public mass transit network onto an existing road network. Unfortunately, even local bus networks in the US pale in comparison to other countries, and certainly to their potential. But they do exist and a non-negligible number of people rely them, especially in more dense cities where car travel has significant downsides. Regarding inter-city travel, I think there are really 2 subcategories to discuss here. If you're thinking about long-distance city pairs like New York to Chicaho, yeah, bus is kind of a last resort. Greyhound (technically now a subsidiary of FlixBus, so there may be some FlixBus-branded buses in the US, but Greyhound is what everyone recognizes) is available nationally, but the schedules and stops are pretty terrible, and the prices aren't really competitive with flying at that point. The people who take those long-distance buses tend to have some other motivation besides cost/convenience, like fear of flying, traveling with children, wanting to take more cargo on a one-way move, needing to make a stop in a smaller city along the route, wanting a certain arrival time that wasn't available by flight, etc. It's rarely the bus option for those sorts of trips from a value perspective. However, there's technically a level of inter-city travel which is much closer to local travel, and buses can be much more compelling in those cases. For example, there are buses from Newark to NYC, Riverside to LA, etc. These are sprawling urban/suburban areas that are much more connected economically and geographically than distant city pairs, and in many cases, the same benefits of local travel extend to nearby cities. For example, somebody who works in San Bernardino but lives in LA isn't going to be able to take a flight, but they might not want to take a car for whatever reason, or they might be hosting family for a week who want to be able to get around for a day but don't want to rent a car for the entire week. In a sense, they're kind of treating these buses like local buses, but just on a larger scale. And then there's one last thing which very few commenters seem to have brought up, but it's actually extremely common in the US. Lots of groups use charter buses. Virtually every national park and other tourist destination you go to in the US, you'll see buses for organized tour groups. They're also extremely common for elderly assisted living facilities because many of those people have mobility issues and the homes like to organize group travel. Summer camps will often bus children to interesting destinations. These are obviously not consistent routes generally available to the public, but they're common enough that I think they're an important point to add regarding bus travel in the US.