Given that lessons in a BYOD environment must be device agnostic, there are a few Web 2.0 tools that I've found I can't live without. Click on the name of each and you'll be redirected to the tool's URL.
GoogleDocs: Students can create a variety of assignments using their Google Drive account. From word processing documents, to forms, to presentations, this is an excellent place for students to complete assignments. You can even create templates to have them copy and modify.
Today's Meet: Students can have virtual conversations using their Internet browser. Open a room for class discussion or have small group conversations in multiple rooms. I recommend that you as the teacher set up the rooms so you can monitor the activity. This can be a very powerful forum for online collaboration.
Socrative: Students can respond to questions posed by the instructor, take online assessments, complete short exercises or exit tickets, and more. This works on any web enabled device, which makes it perfect for BYOD.
Edmodo: An online learning management system, Edmodo is perfect for safe, academic social networking. Students can respond to assignments teachers post, have structured conversations, upload files into a digital locker, and view resources from instructors.
Gaggle: Another online learning management system, Gaggle has all of the features of Edmodo plus a built-in blog for every student and access to filtered YouTube via GaggleTube. Gaggle is a paid service.
Animoto: Both an app and an online video creation site, students can create movie using a series of photos and captions in conjunction with preloaded animation and music.