In the course of developing an in-house address verification service at a German company I used to work for I've come across a number of ways to tackle this issue. I'll do my best to sum up my findings below:
Free, Open Source Software
Clearly, the first approach anyone would take is an open-source one (like openstreetmap.org), which is never a bad idea. But whether or not you can really put this to good and reliable use depends very much on how much you need to rely on the results.
Addresses are an incredibly variable thing. Verifying U.S. addresses is not an easy task, but bearable, but once you're going for Europe, especially the U.K. with their extensive Postal Code system, the open-source approach will simply lack data.
Web Services / APIs
Enterprise-Class Software
Money gets it done, obviously. But not every business or developer can spend ~$0.15 per address lookup (that's $150 for 1,000 API requests) - a very expensive business model the vast majority of address validation APIs have implemented.
What I ended up integrating: streetlayer API
Since I was not willing to take on the programmatic approach of verifying address data manually I finally came to the conclusion that I was in need of an API with a price tag that would not make my boss want to fire me and still deliver solid and reliable international verification results.
Long story short, I ended up integrating an API built by apilayer, called "streetlayer API". I was easily convinced by a simple JSON integration, surprisingly accurate validation results and their developer-friendly pricing. Also, 100 requests/month are entirely free.
Hope this helps!