I had to integrate speech recognition in an App lately. Android phones have google speech which you can use for free, iOS 10 has Siri. However, there was nothing built in for iOS9 and the web. So here's a list of speech recognition services you can try.
Google Speech API
This is proably the best option in terms of quality - even though it's beta. It's priced at $0.006 for every 15 seconds. The first 60 minutes are free
This is the second best option at $0.004 per voice request (of max 15 seconds).
Bing Speech API
I didn't try this but being from Microsoft it must be good. It works out at $4 per 1000 calls of max 15 sec per call - i.e. $0.004 per 15 seconds.
This is actually free and has plenty of libraries.
I liked this one. It's also free. The only problem was at the time of testing the return responses were not as fast as I wanted.
I didn't use this one as the pricing was not clear at the time.
IBM Speech to Text
The pricing for this is $0.02 per minute. They also provide you 1000 minutes free per month. It's pretty cool.
Open source ones that you can install on your server are:
CMU Sphinx: http://cmusphinx.sourceforge.net/wiki/
Microsoft CNTK: https://github.com/Microsoft/CNTK
I found OpenEars not to be so good. I guess these libraries are not as up-to-date and constantly trained as the ones provided as a service.