Beets are in season in temperate climates fall through spring, and available from storage most of the year everywhere else. Fresh beets are often sold with their greens still attached.
Belgian Endive are mostly "forced" to grow in artificial conditions, and are thus available year-round. Their traditional season (when grown in fields and covered with sand to keep out the light), like that of all chicories, is late fall and winter.
Broccoli, like many cruciferous vegetables, can be grown year-round in temperate climates so we've forgotten it even has a season. But, like the rest of its family, it tastes best (that is, more sweet, less bitter and sharp) when harvested in the cooler temperatures of fall in most climates.
Broccoli raabe, rapini is a more bitter, leafier vegetable than its cousin, broccoli, but likes similar cool growing conditions.
Brussels sprouts grow on a stalk, and if you see them for sale that way snap them up - they'll last quite a bit longer than once they're cut.
Cabbage is bright and crisp when raw and mellows and sweetens the longer it's cooked. The cooler the weather in grows in, the sweeter it tends to taste (this effect is called "frost kissed").
Cardoons taste a lot like artichokes; look for firm, heavy-feeling specimens.
Carrots are available from winter storage from local growers in many areas, and fresh in warmer and temperate regions.
Cauliflower may be grown, harvested, and sold year-round, but it is by nature a cool weather crop and at its best in fall and winter and into early spring.
Celeriac/celery root is at its best in the cooler months of fall, winter, and early spring (except in cold climates, where you'll find it during the summer and early fall).
Celery is at its best in the fall, with its harvest continuing through winter in warm and temperate climates.
Chicories are cool weather crops that come into season in late fall (and last in temperate climates through early spring).
Curly Endive (Frisée) is a chicory at its best in fall and winter.
Escarole is another bitter chicory in season fall and winter.
Fennel's natural season is from fall through early spring. Like most cool weather crops, the plant bolts and turns bitter in warmer weather.
Herbs (from hothouses in cooler climates)
Horseradish is at its best in fall and winter. Like so many other root vegetables, however, it stores well and is often available in decent shape well into spring.
Jerusalem artichokes/sunchokes are brown nubs, that look a bit like small pieces of fresh ginger. Look for firm tubers with smooth, tan skins in fall and winter.
Kale is like all hearty cooking greens - cooler weather keeps it sweet.
Kohlrabi (late fall) comes into season by the end of fall, but stays at its sweet best into winter.
Leeks more than about 1 1/2 inches wide tend to have tough inner cores. The top green leaves should look fresh - avoid leeks with wilted tops.
Parsnips look like white carrots and have a great nutty flavor. Look for thinner parsnips, since fatter ones tend to have a thick, woody core you need to cut out.
Radicchio, like all chicories, radicchio is more sweet and less bitter when the weather is cool.
Radishes (large varieties)
Rutabagas also known as "yellow turnips" and "Swedes" are a sweet, nutty root vegetables perfect in stews, roasted, or mashed with plenty of butter.
Shallots from storage bring a sweet and delicate onion-slash-garlic flavor to winter cooking.
Sweet potatoes are often sold as "yams." They store very well and so are available from local sources year-round in warmer areas and otherwise from late summer through winter.
Turnips have a bad rap they don't deserve. Fresh turnips have a sharp but bright and sweet flavor. Look for turnips that feel heavy for their size.
Winter squash of all sorts comes into season in early fall and usually last well into winter.