These are a really great questions! I'm a professional OpenLayers developer and fan, so I'll address your questions from that perspective.
Why would I use OpenLayers instead of Google Maps?
- Flexiblity: You are not tied to any particular map provider or technology. You can change anytime and not have to rewrite your entire code. Google, Yahoo, Microsoft, WMS, ArcGIS Server, MapServer, etc. are all supported out of the box.
- Vector Support: Better support for points, polylines, and polygons.
- Control: You have the ability to add any new features that you may need. I've personally written three plugins for OpenLayers, two of which are or will be part of the source.
- Debugging: Much easier to debug when you can step through the source code!
I would not worry at all about the long-term viability of the project. It is the premier open source client-side mapping library.
Are there any common pitfalls / problems I may encounter?
- The biggest pitfall I've run into is working with the Web Mercator (Google) projection. It can be a pain to display vector data that is in a common and real projection like WGS 84 into an OpenLayers map using Google, Yahoo, and Microsoft base maps. The examples are your friend.
JavaScript Framework Compatibility
- I use the jQuery framework for all of my work, and the only problem I've had is referencing jQuery after OpenLayers. Other than that, it's been smooth sailing.
- Performance is great! The only issues will be with your map server or adding too many vectors to your map.
Are there maps available for many places?
- Like I said, you can use basemaps from just about any source for anywhere in the world.
Is there any kind of API to display roads?
- I'd check out CloudMade! The have converted the OpenStreetMap project into a map tile service and allow custom styling. I believe that you can style one-way streets (per your example) a particular way. The CloudMade Developer Zone.
Do you know any good tutorial to OpenLayers?
I hope this is useful. And I'm around Stack Overflow if you have any questions!