License Plates
Try to see how many different states you can find on license plates. Hint: National Parks are a great place to get several at once. You can also keep track of the license plates that you find of states that you've actually visited.

Scavenger Hunt
Before leaving, create a list of things that everyone has to spot on their way to your destination (i.e. a Maple Tree, a Dodge Viper). Whoever gets the most wins. This can also be played as teams.

Sentence Completion
Have a bag full of slips of paper with sentences to complete (i.e. My worst fear is...My happiest time was...). Each person takes turns drawing from the bag and completing the sentence. You could also have everyone take turns completing each sentence drawn.

Story Building
One person starts a story then passes it after around 20 seconds. Each person has 20 seconds to build the story. See how creative everyone can get!

20 Questions
One person chooses a word (a noun). Everyone else asks "yes" or "no" questions. After 20 questions, everyone tries to guess the answer.

Two Truths and One False
Each person thinks of three statements about him/herself to share with everyone. Two statements are true, but one of them is false. Everyone takes turns telling their statements while others guess which one is false. After everyone has guessed, the truth is revealed. This can be an interesting way to get to know each other better.