The best replacement for requirejs is browserify.

The best alternatives to requirejs are rated as following:
★★★★★  browserify
★★★★★  commonjs
★★★★  require
★★★★  bower
★★★★  grunt
★★★  headjs
★★★  labjs
★★  sprockets
★★  curl
★★  google closure
★  dojo
★  node require
★  curl js

Your alternative for requirejs is not listed? Suggest!
Speaking about requirejs, one probably shouldn't forget about angularjs.

Other search terms related to requirejs and their ratings are:
★★★★★ angularjs
★★★★ backbone
★★★★ bower
★★★ typescript
★★★ grunt
★★★ jasmine
★★ ember
★★ knockout
★ gulp
★ amd
bootstrap
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Google Trends

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requirejs
browserify
commonjs