The answers to the clues below will have something in common.

1. Jilted at the last moment
2. Abandoned at the last moment
3. Stranded runner in baseball
4. Still having questions
5. Politically liberal
6. Insult in the guise of praise
7. Required to figure things out for yourself
8. Disappointing words to a certain fan

Answers:

1. Left at the altar
2. Left for dead
3. Left on base
4. Left in doubt
5. Left of center 
6. Left-handed complement
7. Left to your own devices
8. "Elvis has left the building."