There are many hundreds of online resources that can help you build up your brainpower! Below are a few of the most comprehensive and useful, grouped into different categories (for instance, memory strengthening or vocabulary building).
Category
Resource
Vocabulary and word-building
The Word Search
Washington Post Daily Crossword
Foreign languages
Memrise
Duolingo
Brain teasers and logic puzzles
Riddles.com
Web Sudoku
Luminosity Brain Training
Trivia
Sporcle