I got some inspiration for a mug hugger from someone at work - they had a pattern for a can cozy. It's relatively simple - I just chained until it reached around the bottom of the mug then joined it with a slip stitch then did a whole round of treble crochet. On the next round, I left two stitches at the end, did 3 turning chains and carried on until there was a gap big enough for the handle of the mug. At the end of the last row, I chained two and joined at the top of the handle then did another row of treble to finish off.
I sewed on a rounded off square and stitched a nose and mouth into this, sewed 2 buttons for eyes then a couple of ears :)