General Embarrassment:
* Ashamed
* Flustered
* Mortified
* Humiliated
* Sheepish
* Abashed
* Red-faced
* Self-conscious
* Awkward
* Cringing
* Blushing
* Discomfited
Slightly Embarrassed:
* Uncomfortable
* Ill at ease
* Self-conscious
* Awkward
* Flustered
Deeply Embarrassed:
* Mortified
* Humiliated
* Degraded
* Chagrined
* Shamefaced
* Crestfallen
Specific Situations:
* Caught in a lie: Caught red-handed, exposed, unmasked
* Making a mistake: Floundering, blundering, tripped up
* Being the center of attention: Under the spotlight, in the hot seat, the subject of ridicule
* Social faux pas: Socially inept, gauche, blundering
Figurative/Idioms:
* Face like a beetroot
* Couldn't look anyone in the eye
* Wish the ground would open up and swallow me
* Die of shame
The best word to use will depend on the specific context and the level of embarrassment you want to convey.