|Rivalrous||Private good (MP3 players)||Common-pool resources (timber)|
|Non-rivalrous||Club good (movies)||Public good (lighthouses)|
So a lighthouse is a public good because it is non-rivalrous: if I use the lighthouse to guide me, that doesn't keep you from using it. It is non-excludable: the State of North Carolina cannot prevent anyone from using the Cape Hatteras Light to guide their ships, except by driving them out to sea, which is against Federal law.
Interestingly, the examples of excludability given in Wikipedia all seem to take the community as their universe. A good is still considered non-excludable even if you can exclude people who aren't in the community, as long as you can't exclude community members.
In the most straightforward sense, a train ride is a private good. It is rivalrous because if there's only room for one more person on that train and you get on first, I can't get on. It is excludable because the turnstiles and the transit police can keep people from using the subway. The same is true for buses, cars and bicycles.
But that's the direct benefit to the rider. It is often argued that there is an additional benefit to transit: reducing road congestion. In practice, it has been found that transit does not significantly reduce road congestion. This is probably because when congestion gets bad enough people respond by moving, changing their habits or agitating for more capacity, so the primary benefit of transit to drivers is in reducing road expenditures.
There are indirect benefits: getting more workers to work and consumers to stores instead of driving them away helps the economy run better. Good access to stores and workplaces boosts the success of those businesses, creating more profits and jobs. These in turn raise tax revenue, meaning the government has more to spend. The more efficient the transportation system has, the better use the community makes of land, building materials and fuel. These benefits are rivalrous in the sense that they are divided among members of the community, but they are not excludable because the benefits are available to the entire community. In this sense, transit use is a common-pool resource.
A less car-dependent community has benefits that are non-rivalrous and non-excludable within the community. Reducing pollution, carnage and obesity, and increasing the quality and quantity of social interactions are all public goods that accrue to the community from getting people out of their cars.
This is one of the central challenges of transit: the benefit of transit use is spread across the entire community, but using transit may have a direct cost to individuals that motivates them to resist. A small, focused group of these individuals may be more powerful than the community as a whole.