General:
* Awkward
* Mortifying
* Humiliating
* Cringeworthy
* Uncomfortable
* Awful
* Ridiculous
* Appalling
* Shameful
* Deplorable
* Disgraceful
* Unseemly
More specific:
* For a situation: Awkward, uncomfortable, unfortunate, unpleasant
* For a feeling: Mortified, humiliated, ashamed, self-conscious, sheepish
* For an action: Awkward, gaffe, blunder, faux pas, mishap
The best synonym will depend on the specific situation and the level of embarrassment you want to convey.