The best replacement for checkboxes is radio buttons.

The best alternatives to checkboxes are rated as following:
★★★★★  radio buttons
★★  multiple select
★  check boxes
★  option buttons

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

Other search terms related to checkboxes and their ratings are:
★★★★★ form
You have in mind a companion for checkboxes and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of checkboxes in all years. Click on graph for more.
checkboxes
radio buttons
multiple select