Tips I thought were most useful:
1. Movie times: either type in the name of the movie and your zip code, or just type "movies" and your zip code
2. Time zones: type "time" and a city's name (or zip code) to find out what time it is there
3. Related searches: add a "~" in front of a word (e.g. "~nutrition" will turn up searches for food, nutrition and health)
4. Exclude words from search: add "-" in front of word to exclude it from the search (e.g. "dessert -cookies" will search dessert but exclude finds that include cookies)
5. Conversions: "5 miles in kilometers"
6. Flight status "Delta flight 5778" tells you if it's on time
7. Specific image searches: UPDATE: Google Image now has a handy drop down menu to let you choose what type of picture you want to search (news, photo, face, line drawing...) - Very handy!
8. Track UPS/FedEx shippings by entering in the tracking number
9. Search college sites by adding "site:edu" to the end of the search (probably works for gov also)
10. Definitions: "define: word" gives a definition of the word
11. Weather: "weather 12345" gives the weather in zip code 12345
12. GoogleFight.com: let's you type in two key words, then tells you how often each one is used (e.g. "hunger pains" vs "hunger pangs" - pangs wins)