The best replacement for mugs is cups.

The best alternatives to mugs are rated as following:
★★★★★  cups
★★★★  steins
★★★  coffee cups
★★  paper cups
★  glasses
★  coasters
★  bowls
  disposable cups

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

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



Google Trends

Scale is based on the average worldwide traffic of mugs in all years. Click on graph for more.
mugs
cups
steins