The traditional type of sushi, before maki (rolls) became the norm. Many places simply call nigiri "sushi" and rolls "maki", so be careful when ordering rolls that you specify since to many native japanese people sushi translates only to nigiri.
This form of sushi is generally preferred by those who have a taste for raw fish, and it provides a much higher ratio of fish to rice than rolls do. It is also healthier and lower in calories since there is more protein and no fried or mayo'd product.
The most popular is salmon nigiri, closely followed by yellowtail nigiri. Both have a very mild, nearly buttery flavor and so are also ideal for first-timers.
There is also sweet shrimp, which is raw shrimp, and fish eggs (salmon roe or flying fish roe) which are popular options.
If you have so far only had rolls when it comes to sushi, it would be a good idea to try out the nigiri version as well, you might like it more! But be warned, once you're addicted you can never go back.
White Tuna nigiri
Sweet Shrimp nigiri
Flying Fish roe nigiri
If you are adventurous, try the sea urchin. It's an acquired taste, but has been found to contain the same chemical that makes you high when you do pot.