No, you do not need to purchase any additional equipment if you have a Sonos speaker. Sonos equipment is made to be simple. It is self contained, easy to set up, and controlled by an app controller that works over your wireless network without extra equipment being added.
Most equipment including the Soundbar, Play:1, Play:3, and Play:5 can operate entirely on their own. Sonos does make ancillary equipment such as the Boost and Connect, which are meant to be used with other equipment. The Boost works as an alternative to your home WiFi network in case you are experiencing interference. The Connect works with your existing stereo equipment which does not necessarily need to be from Sonos.
While you can use a controller over the internet from a webpage, it is recommended to download the app on your smartphone or tablet so that you can control your equipment from a mobile device, which is more convenient.
Ultimately, Sonos was created so that people can mix and match their equipment easily in order to build increasingly complex sound systems. The amount of speaker equipment that you add is entirely up to you, but all Sonos speakers come with their own drivers and amplifiers, and they are controlled over the wireless network.
Using A Boost
There are some cases where your home WiFi network may have interference, the signal may not be strong enough through your house, or it may not have the bandwidth required to handle the amount of music or sound that you are asking your speakers to play. In these cases, you may need a Boost, which works like an ancillary wireless network on which only your Sonos equipment communicates.
If you are using multiple speakers and if they are spread over a large area in your home, and if you are having any issues with the quality of sound such as pauses, skips, or communication issues, you may need to add a Boost to clear these issues up.