Tell me some interesting tomato sauce variations.

Another way to broaden your search. Soups and sauces are closely related - cousins if not siblings - in technique. Many soups are thinned or more liquid versions of sauces.
So if you're looking for new tomato SAUCES consider recipes for SOUPS using tomato as a prime or main ingredient.
Then, make as directed if you like the idea of soup (also can add pasta or serve with bread).
Or make them thicker and use as sauces.

As a few have suggested, tomato really goes with almost anything, and the best way to go is to think of a regional cuisine and take it from there :
- Spanish influenced: tomato, orange, saffron
- North Indian: tomato, ginger, garlic, turmeric +/- garam Masala
- More South Indian influence: tomato, mustard seeds, fenugreek
- Tomato, cilantro, onion was a childhood favorite pasta sauce
- Tomatoes simmered with red and yellow peppers, and a bit of coriander powder is an Algerian favorite
- Tomato, celery, cilantro, carrot, zuchhini forms the basis of a widely eaten Algerian/Morrocan soup (usually with orzo pasta or vermicelli cooked into the soup)
- Southern France: tomato, parsley or tomato and shellfish
- I've used tomato with beetroot to great effect in pasta sauces when I needed to clear out the fridge
- Don't forget the fresh (as opposed to cooked) tomato sauces that are basically like salsas
And the list goes on...

Vodka sauce is always a crowd stopper. It is in essence tomatoes with heavy cream, garlic, and vodka. Another sauce to check out is peperonata. Tomatoes take a back seat in this one. It is roasted red bell pepper, garlic, and tomatoes.

I'd say Puttanesca and Amatriciana (two of my favorites,) but they're classics, so probably not what you're after.

I make a 'Greek-ish' tomato sauce with ground lamb, onion, garlic, oregano and a touch of cinnamon (sometimes cubes of eggplant sauteed in with the lamb/onion/garlic too.) Served with pasta and crumbled feta on top, instead of parm. Very tasty.

As many have remarked, tomato is a great combiner. In addition, or for emphasis, to the ones already suggested, go by country cuisine and cook what you like with tomatoes:
Congo/Africa - chicken in tomato peanut butter stew
Eastern European Jews/Hungary - various cabbage soups with tomato added
India - various tomato chicken curries
Enjoy...:)

One more idea. We make a sort of generic tomato sauce and can or freeze it - just the basics - tomatoes onion, garlic etc. Then, we we need it we add other things. The coolest thing we tried already this year was this - we puréed basic in olive oil and froze it in small portions. Just added it to tomato sauce - oh baby! Also (for another question) squeezed it into a frittata. Just like summer.

Try yellow tomatoes instead of red, with a pinch of basil and a dollop of cream.

Blend it with feta cheese, or a soft goat cheese, it makes the sauce tangy and delicious. I would also add a little bit of mint to that.

i made tomato sauce last night for a base for a variation on chiles rellenos. Onions sauteed in butter or oil (depending on your taste), canned whole tomatoes, pepper, cinnamon, bay leaves, salt, cloves, and garlic. Puree with a stick blender after it has reduced down, and use as sauce for chiles rellenos.

I make this tomato base sauce often, Tomato Sauce With Capers and Vinegar, an NYT recipe. Whenever I want a change in flavors, I add piquillo peppers, roasted peppers, pancetta cubes, vinegar, cream, chipotles in adobo, capers, caperberries or anchovies.

What do you want to use the tomato sauce for? Are you thinking pasta or going in a different direction?

Mallika's tomato curry sauce is on my list to try. Has anyone made it?

Huge subject- could (and no doubt has) fill several books. I would suggest, as a generality, that tomato works well with virtually any sort of pepper and any sort of herb. In fact it is one of the great combiners.

A couple of things come to mind - a Shakshuka type flavor profile - cumin, paprika, cayenne, mint - you could flavor your sauce and serve it with feta instead of parmesan,

I really like the combination of tomato and orange, which would be great with a seafood pasta and freshly chopped parsley.

And of course, being a Texan, I have to suggest a smoky chili flavored sauce (think anchos, chipotles in adobo, etc), maybe made with sausage and served over grits or polenta ....