Are there some statistics out there that show the approx. number of users that popular programming languages have and the rate this number increases over time?
Programming language trends are notoriously hard to make sense of, and all available statistics & metrics should be taken with a grain of salt.
One of the most oftenly quoted indexes is the TIOBE Programming Community Index, that rates programming languages by counting hits on the most popular search engines. As for job trends, Jobs Tractor publishes monthly trends, based on listings for developer jobs.
If you are looking to compare specific languages against each other, Ohloh provides a very handy language compare tool, which counts monthly commits by open source developers. You can also use Google Trends, for example here's a comparison of Haskell vs Scheme.
You can always look at Stack Overflow, and more specifically at the language tags, or popular code hosting services like Github, that maintains a "top languages" page. And if you are a Redditor, look no further than /r/programming's FAQ.
As you may have noticed, all the available data seem quite unreliable, and that's understandable, popularity is extremely hard to measure. And, at the end of the day, popularity and trends are rather irrelevant metrics. Who cares which language is the more popular, programming languages are tools, if it does what I need it to do, it's fine by me.