Most vegetables grow well in a greenhouse environment. A greenhouse lets you artificially control your garden all year round, even in the coldest months. You still need to keep temperatures in mind when you plan what to plant at what times, but fresh vegetables all year is entirely possible with a greenhouse. The biggest consideration in determining what grows well in a greenhouse is space. Even the largest greenhouse is not big enough for plants that spread out wide such as watermelon, and space eaters like corn.
Unless your greenhouse has climate control, outdoor temperatures still control you to some degree. Sunlight is easier to conquer with growing lights, but heat and humidity are tough. It is better to adapt your greenhouse growing desires to cool loving plants in the winter. Protected from the outside elements and deep freezes, and given enough light, both natural and artificial these vegetables thrive in winter greenhouses. Lettuce, broccoli, cauliflower, spinach, and other leafy vegetables that burn easily in the heat of the summer are wonderful winter vegetables. Root crops like carrots and onions do very well in winter months inside.
Typical summer vegetables do well in a greenhouse in early spring and late fall when they would not be able to thrive outside. Tomatoes, squash, eggplant, and peppers are easy to grow indoors. Keep an eye on the temperatures and humidity during the hottest parts of the summer. Even these heat lovers can get overwhelmed by a closed off greenhouse. It is easy to regulate the summer temperatures with proper ventilation.
Certain vegetables can even do well all year. Tomatoes are a popular greenhouse vegetable that will perform reasonably well in all seasons. Peppers and cucumbers are close behind tomatoes in popularity and ease. Lettuce is more difficult to grow in the hotter months, but if you use enough shade and ventilation, it will do fine all year round.
Look for varieties of any popular vegetable created especially for greenhouse environments. Any variety will do well, but varieties created to thrive indoors will do even better and produce at higher volume. Vegetable varieties created for greenhouses are also less prone to disease the heat and humidity of a greenhouse can produce.