Get thee to your local Asian grocer!
Zarusoba is a dish of cold buckwheat noodles served with a dipping sauce filled with green onions, grated radish, and wasabi. It’s great with tempura (in which case you’re eating ten-zaru). This is a good, basic recipe.
Sōmen are thin wheat noodles served ice cold (or even on ice), with a dipping sauce (look for mentsuyu in the grocery). Paired with hiyakko, it makes either a light meal or a filling snack.
Yakisoba is similar to lo mein–basically stir-fried noodles with shredded cabbage, julienned carrots, sliced mushrooms, and whatever sort of meat or fish you’re into (or none at all; I enjoy it with just the vegetables). Asian groceries will carry both the noodles and yakisoba sauce–but be aware that the sauces contain lard (even though the English ingredient lists don’t always mention it, the Japanese copy on the packaging will say things on the order of “Chock full o’ lard!”).
Now that I’ve made myself hungry and nostalgic, I think I’ll make miso ramen for my breakfast.
Enjoy!
I almost forgot about japchae. To save on calories, I make mine with shirataki instead of the cellophane noodles commonly used in the recipe.
The site I linked to above, Aeri’s Kitchen, is wonderful, and not just for Korean noodle recipes. 
(I wish there were a Hungry, Hungry Hippo smilie!)
My own favourite and simple.
Once your noodles are almost done, put them in a saucepan with some milk, some butter and a bouillon cube.
Stir (low fire) until everything is disolved.
Nice, simple way to enliven a simle dish.
One of my favourite no-tomato pasta additions is mushroom-spinach-walnut pasta sauce. Basically, sweat the moisture out of a heap of sliced mushrooms and some chopped onion, add a bag of chopped frozen spinach and allow it to melt and some of the moisture to evaporate, while chopping a handful of walnuts. Add walnuts and a splash of single cream, season to taste.
Here’s my party pasta recipe from my student days, kind of a primavera recipe with a cheese sauce. Start off with getting some pasta on the boil and micowave a bag of frozen peas. Sautee diced mushrooms and diced zucchini (you can add ham at this point) until softened, add peas and season with salt and black pepper. Drain the pasta, put about 1/4 cup of single cream per serving into the empty pot and put it back on the stovetop (low temp, usually the residual heat was enough). When the cream boils, add mature shredded cheese and stir until melted. Add pasta + vegetables and stir thoroughly.
I’m fond of the cold, sesame/soy sauce based noodle dishes, and would suggest adding ginger (either finely chopped or press a larger piece for the juices). It’s very refreshing. I usually use buckwheat noodles though they’re relatively pricey.
My mom does a very simple lo-mein for potlucks, which is tasty and user-friendly. Heat some oil (enough to coat your pasta) in a wok, and add chopped green onion and cilantro. Cook till fragrant, then add cooked spaghetti and stir together. Take the pan off the heat and add oyster sauce (enough to coat the spaghetti, but not so the noodles are slippery). Add pepper and a bit of salt if desired.
…And I must confess, this is usually the part where I taste the noodles and scratch my head a bit, because it still doesn’t taste as good as when my mom makes it. I might skimp too much on the oil…
You can also saute some veggies (onion, snow peas, thinly slices carrots and celery) and chicken for a complete dish.