I steam green beans, broccoli, asparagus, beets. But you can also (as pretty much everyone said) roast basically anything. In the winter it is my go-to way because I don't mind using the oven and making the house warmer. Roasting really concentrates the flavor and is so easy.

What do you mean by healthy? Low fat? Because some fats are not only healthy but add much flavor to vegetables.

Some favorites:

Brussels sprouts, roasted or sauteed in pan. Olive oil and/or butter may be used. Carmelize onions or shallots first, remove from pan. Saute the sprouts (halved or quartered) until they are tender-crisp and a little browned. Add in the onions or shallots. Other nice additions are walnut pieces, parmesan cheese, or bits of crispy bacon.

Ratatouille - great way to use up late summer veggies - eggplant, summer squash, peppers, tomatoes, garlic, onion, lots of olive oil, some salt, pepper, maybe paprika or parsley. Check out some recipes to find one you like. Can be served hot. When I make it I cut everything into fairly small pieces, so that after I refrigerate the leftovers, it makes a very good dip with pita chips or better yet lavash.

You could make some Asparagus Thoran.

I really like dark leafy greens if they're prepared by sautéing them (along with either onion or shallot) in a little olive oil. I then load them up with salt, pepper, and vinegar (cider / red wine / etc.).

Stir fry is a winner for vegetables, and how about soups? I made a soup with my son the other day that easily had 7 cups of veggies in it. He loved it, and he is NOT a veggie fan. (Think minestrone, served with some parmesan on top, yum!)

I steam then sauté with a little bit if olive oil. I then add braggs amino acid (it taste kinda like soy sauce but less sodium and better for you). If my sweet tooth grabs a hold of me, I drizzle some aguave nector or raw honey on top

Definitely roasting. Also sprinkling with parmesan and/or adding bacon.
Pinterest is great for recipes that may tempt you to try them.

Roasting in winter, grilling in summer. Yum!

Make a stir fry. Add lots of vegetables. Cut back on oils and fats.

Agree on roasting. Or throw them into a smoothie with fruit so you don't taste them!

OP Here thanks all! Roasting it is! We have an awesome toaster oven so I roast a lot (especially butternut squash lately). I'll just start tossing things together and see what works!

Roast them!

Google for many, many recipes but in a nutshell: Chop veggies -- broccoli, carrots, cauliflower, Brussels sprouts, squash, asparagus, green beans, etc. Literally anything that looks/sounds good. Toss with a bit of olive oil (olive oil spray works too). Spread evenly on a baking sheet (I line with foil or parchment for ease of cleaning) and sprinkle with salt, pepper, and anything else in your spice cupboard that sounds good. Roast at 400 for half an hour or more, until veggies are tender.

Roasted veggies are very forgiving -- experiment freely to find what tastes good to you! 400 degrees is not set in stone -- I've gone higher or lower depending on what else is in the oven. They also keep well -- I like to add them to salads for lunch throughout the week.

Try some of the "Healthy" (Healthy Weight, Healthy Vision, etc.) microwave mixed vegetables that Green Giant puts out. They're pretty tasty. I take them to work and eat them for lunch. I really, really like the Healthy Weight mix (black beans, edamame, carrots and sugar snap peas)

If you like your veggies raw, there's nothing wrong with having a salad with every meal (and there are plenty of ways to mix it up and have a different combination/flavor every time)
Roasting veggies is our new favorite and with colder weather coming, it is the best time of year to start trying it. You can roast brussel sprouts , cauliflower, potatoes, sweet potatoes, onions, peppers, eggplant, winter squashes, carrots, parsnips, beets, turnips. Just cut them in pieces and brush with olive oil and S&P and roast in the oven for 20 min or so at 400'ish. You may want to check in the middle and turn/stir them. We often put veg and chicken pieces on the same baking sheet and dinner is done in one pan.
Green beans and broccolli are best simply steamed until just done and still crisp. Eat as is or add a sauce/seasonings.

You can roast lots of things - asparagus, brussel sprouts, broccoli, cauliflower... space them out in a single layer, cut bite sizeish, drizzle with olive oil and salt and pepper. 375 until they brown. About a half hour depending on the veggie.

This is my method for bok choy - http://www.steamykitchen.com/2112-bok-choy-stir-fry-recipe.html

I like to grill green beans in summer, but indoors, sautee with lots of garlic, maybe a spritz of lemon juice after.

Plain and simple I need to learn how to cook them in a healthy way that I will like them.

I'm not a huge veggie fan, I never had been and my parents for some unknown reason didn't force me to, not even to try them... Either way, I'm an adult, I enjoy squash and can cook them well, but I need to learn how to cook things like green beans, asparagus, brussel sprouts, bok choy, etc. Obviously I want to cook them healthy, so oven roasting, pan roasting, etc. Ideas or suggestions? I've got a few good cooked carrot recipe's, but have found I much prefer them raw