If you knew them, yay! If you didn't know them, then...
All screenshots were taken on the 6th July 2014, so the information on them is probably not relevant now.
1. Sports team scores
If you follow US sport (for example Major League Baseball), then you can just type in the name of any sports teams participating in such sports and see how they stand.
For example, I typed in Boston Red Sox (the only US sports team I know, thanks to my many wasted hours of watching Cheers), and this is what came up...
I have no idea what any of that means.
2. The time anywhere in the world
If you type in 'time' and then any city in the world, it will tell you what the time is. Furthermore, if you type in 'what's the time?', it will tell you the time in your current location.
3. The Stock Market
For those of you who are stuck in the 80s/a fan of the stock market, you can type in the ticker symbol for any stock-holding corporation and it will tell you its current progress in the stock market. For example, I typed in MSFT (the ticker symbol for Microsoft Inc.) and this is what came up...
4. Unit conversion
You can convert between many different units of mass, length, volume, etc. by typing in for example "450 mm in km" or something. You can also do this for currency by typing in, for example, "100 GBP in USD".
5. Searching certain websites
If you want to search results solely by one website, then typing in for example "site:website.com" after your query can search only for results within that website.
6. Aeroplane flights
By typing in "flights from x to y", substituting x and y for locations of your choice, Google will tell you the approximate length of the flight and show several options for available flights. You can also see the flight status of any flight by typing in the airline and the flight number immediately after it (with a space sandwiched between them, of course).
7. Dictionary and thesaurus feature
You can find the definition of any word by typing "define" and then the word you wish to define. A list of synonyms and antonyms comes up as well as an example of the word in a sentence to accompany the definition. You can also use this feature to observe the etymology of words & the popularity of the word over time, and to translate it into different languages.