The best replacement for yui is jquery.

The best alternatives to yui are rated as following:
★★★★★  jquery
★★★★  dojo
★★  gwt
★★  extjs
★  jquery ui
★  closure
★  prototype
★  ext
★  backbone
★  mootools
★  uglifyjs
  google web toolkit
  miaka
  spry
  blueprint
  iwasawa
  scriptaculous
  backbone.js

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Google Trends

Scale is based on the average worldwide traffic of yui in all years. Click on graph for more.
yui
jquery
dojo