Issues with apache + nghttp2

For quite a while now, apache-2.4 can make use of the http2 (SPDY) protocol via nghttp2 package.
Unfortunately I had quite some trouble getting the protocol to work on my apache webserver and I couldn't figure out what the issue was until I enabled debugging for that module:
${EDITOR} /etc/apache2/modules.d/41_mod_http2.conf

Replace the line
# LogLevel http2:info
with
LogLevel http2:debug
and restart your apache server. Now try to access some site that should be served via HTTP2. After doing so, grep the apache log files for the following string:
grep -Fr "http2:debug" /var/log/apache2
and you should most likely find the problem with your HTTP2 setup.
Don't forget to disable debug logging again or else your log files will quickly become huge.

In my case it was a cipher combination that was not allowed to be used for HTTP2. After disabling the specific cipher, HTTP2 finally worked on my apache.