What can be used as a substitute for tomato sauce in typical italian dishes?

You could use Red Pepper Coulis:

Roast red peppers on grill, gas flame or cut off the sides and place skin side up under broiler until skins are blackened. Cool and remove charred skin.

Sweat onions and garlic in a little olive oil with salt and pepper until softened. Add the charred roasted red peppers and some chicken stock. Simmer until vegetables are very soft and puree with an immersion blender, food processor or regular blender. Taste and adjust seasoning as necessary. Thin with additional stock according to consistency desired/needed.

Add basil, oregano, Italian seasoning blend to season as desired.

A big component of pizza sauce has nothing to do with tomatoes per se. Break down the components and consider alternatives.

Water: Yup, tomatoes are just wet, so you'll need some liquid.

Sugar: Tomatoes are naturally sweet, so you'll need some sugar/honey

Acid: This is huge, but easily fudged with vinegar or lemon juice

Seasonings: As much onion (powder), garlic (powder), salt, pepper, basil, oregano, parsley as you want

Depth: This is the tricky part, that rich, almost smoky quality of cooked tomatoes. It won't be easy to replace. Darin's answer probably comes closest with a similarly colored pepper cooked with direct heat. To expand on that, I think you could venture into other peppers besides just red bell, maybe some mexican low-heat varieties, a little chipotle, perhaps?

I have used red beets (canned), which I have diced very small, and cooked down with other italian ingredients ( minced garlic, onions, spices, etc.). Also add a bit of vinegar, since tomatoes do have an acidic flavor. Cooked as you would normally cook a spagetti sauce, it is almost impossible to know the difference.

My wife has a sensitivity to night Shade vegetables which includes tomatoes and most peppers. You can look it up. I make her pizza with pesto sauce and it's quite good. I am, however, still looking for other alternatives to tomatoes in sauces.

Great question. I'm not sure there exists anything quite like a tomato, I'd like to hear others though.

Specifically addressing pizza though, and avoiding white sauce, you can make a very yummy pizza just topping the dough with olive oil, garlic, and mozzarella. You can really go anywhere from this base.

Since cheap ketchups are generally made of apple puree, vinegar\acid, sugar, salt (plus thickeners and spices and preservatives), I'd try to create "tomato" sauce of your own from apples and capsicums. You can also add some powdered paprika for red colour. Herbs, garlic, salt, pepper, sugar, vinegar as well:)

Roasted "Kent " or "Jap" pumpkin brings out a nice nutty flavour which can be puréed as well. Good for pizza bases - obviously cooked spices mixed in will also enhance the flavour to be more bold and take away from the "sickening" flavour of pumpkin that some complain about.

I have made a pumpkin based pasta sauce for many who "hate" pumpkin - and all but one finished the entire meal and enjoyed it!

I think a combo of eggplant, squash and roasted red pepper, all skinned and boiled down the pureed, with the onions garlic and spices is probably the closest thing i have made to replace tomatoes.... It is a terrible thing to lose the taste of tomatoes but this ^ is a great alternative.

Buy California chili powder, usually in the Mexican isle in your local grocery store, add some of the powder to water, not to much, add a decent amount of salt and a bit of lemon and onion powder if desired and it tastes exactly like tomatoes! Note the California chili powder is not at all spicy.

Alternatives that I've enjoyed in the place of sauce are...

(1) Pea Puree (which, if prepared with cooked onion and herbs and oil can be slightly sauce like...)

or, as have already been suggested

(2) Pesto, predominantly basil ... though somewhat heavier and saltier than sauce (because of the parmesan and/or nuts)

In both cases, balsamic vinegar can provide some of the acidity that tomatoes offer.

I have certain food allergies myself. While I'd be careful when doing any kind of experimentation, the more processed the food, in general, the less allergic I am. I imagine highly processed ketchup's might be ok. But I'm no medical expert, of course.