Veggie leftovers, now what?

If they're cooked and seasoned (I'm assuming, since you said "leftovers") then chop them small and add to a sturdy lettuce or spinach (pre-dress the greens with a touch of oil, salt and pepper) for a salad. Add a tart/mustardy dressing on top and you're good! Not to self-promote, but I do this all the time and document it at itsasalad.tumblr.com (I'm bad about tagging but anything tagged #cookedandraw is a take on this idea). Cheers to veggies--they make you powerful!

Or there's Tamar Adler's solution -- take any and all vegetable matter, chop it up and serve on toast with a drizzle of good EVOO and maybe a little shaved cheese, or some minced herbs (though maybe potatoes on toast would be overkill!).

My usual options have been mostly covered, I have a few more.
A hash brown type dish, or one modeled after a fried rice recipe;
a veggie burger -- mash everything (food processor or hand), add a thickener if needed (flour type or flakes like oatmeal, maybe an egg); salad: add a dressing you love, toss and marinate (maybe some raw ingredients like cukes, radishes, for a crunchy contrast). Or I'll just reheat ingredients and toss with one of the orphan sauces or condiments I have. Usually, delicious combinations result that you never could have planned.

Make a burrito. Mix with scrambled eggs or tofu, cheese, salsa. Voila, breakfast burrito. Or lunch. Or dinner.

Soup & frittata are great ideas! I do it all the time!
I often take leftovers like the ones you list, throw them in a pot with some stock and simmer till they are soft then I puree into a soup. My husband always looks forward to the "Thanksgiving Soup" that I whip up every year after the holiday. I will say that if you don't stop to think a minute about what is going into the soup then the color of the finished product could be less than lovely. Depending on the type of bean you may want to hold them out. You could toss them in with some rice or barley or any grain for a nice side dish.

If they aren't too mushy, you could make a frittata. Just reheat gently with olive oil in a skillet, pour in some beaten eggs with cream , and a dash of herbs of your choice. Viola! Dinner!

Perhaps purée the carrots and cauliflower, serve the rest of the vegetables over some quinoa or rice (if also leftover, more's the better), and drape the carrot-cauliflower sauce over it all.

Toss them with a simple vinaigrette. And I feel like a broken record with the frittata suggestion, but I think its a great canvas for leftover "stuff." The cauliflower, carrots, and onion would also taste good mixed into a rice dish.

Make soup! This one has a good base. http://food52.com/recipes/2444-very-veggie-soup

Those would make an excellent curry.

Are they mashable? you could mix them with salmon, eggs, spices, bread crumbs and make patties that you fry and serve with buns and sauce.