The following is a list of my personal favorites in different categories.

Arab and assorted Middle Eastern
Carthago in Nakano. Expensive, but usually worth it. Otherwise, a cheap and valid alternative is Shamaim in Ekoda.

Belgian
Brussels in Harajuku and Kagurazaka, of course. No better place to have Belgian beer and fries.

Burmese
Yatana in Shin Okubo. All the more so now that it has a Karaoke-free room at the second floor.

Cajun
Bourbon Street in Roppongi

Cambodian
Cambodia in Takadanobaba. Certainly not Angkor Wat.

Chinese/Taiwanese
Tainantamii. Various locations

Country & Western
Lone Star Café. Note that I do not recommend it for its food but for everything else. Read the review and you will understand.

French
Brin De Muguet in Ogikubo
Also excellent and underpriced is La Sucree in Asagaya.
If you feel like crepes, go to Le Bretagne.

German
Bernd's Bar in Roppongi

Indian
Nataraj in Ogikubo. Best vegetarian and best Indian restaurant in town. An equally good Southern Indian restaurant is Dhaba India in Kyobashi.

In Takadanobaba, my favorite is a Bengali restaurant, Tetulia.

In Kamakura they have one of the best Indian restaurants in Japan, T-Side.

Italian
Superbacco and Il Bacaro are both excellent and unique. They are not Italian, but rather VENETIAN restaurants.

Taverna in Takadanobaba is by far the best in terms of price/performance ratio.

La Cantinella among the very expensive is good for its Southern Italian dishes.

In Kamakura and Zushi, respectively, A Riccione and Lanterna Rossa.

Indonesian
Jembatan Merah in Ikebukuro

Japanese
In terms of sashimi and other fish, my favorite is hands down Najima in Hayama. There are no restaurants as good as that in Tokyo.

Lao
Lan Saang in Kichi Joji

Nepali
Yeti in Takadanobaba
Namaste Katmandu in Kichi Koji

Pakistani
Marhaba in Ikebukuro. This is one of the best restaurants I know in any category. Go!

Peruvian
Romina in Yotsuya

Spanish
Tio Danjo in Ebisu for its food. Order its olives.
Meson Madrid in Higashi Nakano for ambience.

Thai
Kao Tai in Takadanobaba.
Bangkok in Roppongi.
Lan Saang in Kichi Joji. It also has Lao dishes (the owner is a Lao).
Mekong in Ikebukuro

Turkish
Istanbul in Shinjuku
Izmir in Asagaya

United States
Kua'aina. Various Locations. If you want a hamburger with fries, let them be Kua'aina's.