The simple answer is yes. It's a natural part of the growing process that our teenaged children (or even pre-teens) want to show their individuality and their independence from their parents. They have their own ideas about what's acceptable behavior for themselves and their parents, not to mention acceptable clothing, music, hairstyles and almost everything else.
One of the things teens find most embarrassing is displays of affection. Boys in particular tend to be mortified if anyone (meaning their peers) should see you hugging or kissing them -- or worse, expecting them to kiss you! They want their friends to see them as independent and grown-up, not "babies" whose parents look after them. For the same reason, they'll often ask you not to drop them off or pick them up right in front of school/a party/a game/a friend's house. On the other hand, offering to drive your teen and his or her friends to where they want to be can earn you gratitude from your child -- so long as you're not seen or heard.
Teens are often embarrassed by how their parents look -- what they wear, what car they drive. They see themselves as part of a new generation with different concepts of style and fashion, and they don't want to be associated with someone as old-fashioned and uncool as you. On the other hand, teens don't usually want their parents to be too up-to-date. You really don't belong to their generation and they won't want you barging in on their territory.
Anything that draws attention to you in public is likely to make your teen cringe: singing out loud, dancing in public, any show of romantic interest between you and your partner. Teens tend to imagine that they are under scrutiny at all times, and that they are being judged on not only their own behavior, but also that of anyone connected to them.