On the left bank in the Latin Quarter/St Germain area, I have some favorites eating spots:

Patisserie Viennoise.  8, rue d l’Ecole de Medecine.  Metro: Odeon.
What a classic pastry shop!  I go out of my way to have breakfast here.  You can sit down inside if you wish.  The world’s 2nd best hot chocolate.  Closed weekends.

Bistrot d’Henri, 16, rue Princesse, 6th. Metro:  Mabillon or St Germain des Pres or St. Sulpice
This is a very popular and friendly spot.  The tables are close, but that’s fine because everyone there always seems to be social and willing to share their travel stories.  The food is very good.  My lunch (for 2) costs 54 euro with wine.  Lunch cost me 54 euros for two here in February.
For a variety of inexpensive restaurants with good food and service, go to rue Grégoire de Tours between rue Buci and Boulevard St. Germain and get off the Odeon metro stop in the 6th, .   My particular favorite is Au Beaujolais at 9 rue Grégoire de Tours.  It is a good value for your euro and you’ll have fun, too.  Make sure you see Hakim and mention my name.  

Le Pré Verre.  8, rue Thenard, 5th.  Metro: Maubert-Mutualite.
You know it has to be good if the Parisians line up to get into the place.  Near the Cluny, across the street from the Hotel du College de France.   They have a prix fixe dinner for about 35 euro each that includes wine.  Lunch costs half of that.  Make a reservation a day or two beforehand.   This is the best value in Paris.   Check out the Hotel du College du France across the street for you next stay in Paris.   http://www.lepreverre.com/

Rue Buci:  There is a Salon de The which is good for breakfast.

Le Coupe Chou.  9-11, rue de Lanneau, 5th.  Metro:  Maubert-Mutualite.
Americans seem to love this place located in the Latin Quarter.  It’s romantic, it’s very French, it’s reasonable, and the food is good. Usually you don’t need a reservation.  You’ll pay about 100 euro for two. http://www.lecoupechou.com/

Café Constant. 139, rue St. Dominique, 7th.  Metro:  Ecole Militaire.  Casual.  Great food.  Get the “flotante” for dessert.  Near Champs du Mars and Rue Cler.  110 euro for two.   http://www.leviolondingres.com/eng_news.htm

On the right bank, I like:

Chartier.  7, rue Fauborg Montmartre, 9th. Metro: Grands Boulevards.
Fun and cheap.  I eat here at least once every time I go to Paris.  You may find your self sharing a water bottle and bread basket with a Parisian or someone from Finland, Warsaw, Buenos Aires, or Tokyo.   The food is not the best, but go here to eat as the Parisians have been doing for about 100 years.  It’s a lot of fun.   You can get an appetizer (called an entrée in Paris), a plat (what we call an entrée in the U.S., dessert, wine (or water) for about 20 euro each.  No reservations, just line up outside and chat up the friendly crowd as you wait to get in.  They stop seating at precisely 10 pm.    http://www.restaurant-chartier.com/www/visit/filsdesans.php

Aux Lyonnais. 32, rue St-Marc, 2nd. Metro:  Bourse or Richelieu-Drouot.
An Alain Ducasse restaurant for 100 euro for two?  You bet. Top!  You need to reserve a day or two ahead of time.  http://www.alain-ducasse.com/public_us/cest_aussi/fr_aulyonnais.htm

Bofinger.  5, rue de la Bastille, 4th. Metro: Bastille.
A turn of the century Parisian favorite.  Even though the crowd is mostly French, I found the management and waiters to be quite friendly and accommodating.  Near the Opera and Bastille.  Moderate.  It’s near the opera house, so it’s difficult to get a table before or after the opera.   You need to reserve a day or two in advance.  Probably about 125 euro for two.  http://www.bofingerparis.com/

When I was strolling around the Marais in February, I noticed a few very nice restaurants with price fix menus of 20 euro or so that were empty.   The economy has hurt the restaurant business badly.

L’As du Fallafel.   34, rue des Rosiers, 4th.  Metro:  St. Paul.
A Jewish deli-type of restaurant in the Marais.   I like it so much for their 5-7 euro Fallafels (they call them “Cocktail de Viandes” which literally means “Meat Cocktail) that I keep their business card tacked on my corkboard in my kitchen.   A great little take-away (“emporter” in French) place or fine for a sit-down lunch.  Right now, it is one of the most popular eating spots in Paris.  It is not fancy at all.