Of all vegetables? Hard to compare carrots to peas. :) Things I won't do without:

Sun Gold and Black Krim tomatoes (yeah I know they aren't vegetables)
Vidalia onions
Cheddar Cauliflower
Rose Finn fingerling potatoes
Buttercrunch lettuce
Silver Queen corn
Jersey asparagus
Butternut squash

Dave

You don't say where you are, but for some of the warmer weather crops, the best varieties are the ones that produce for me in my highly variable weather.

However, ones I like for flavor:
King Richard Leeks
Sugar snap peas (and I've tried 5 or 6 snap pea varieties, but sugar snap have the best flavor)
San Remo canning tomatoes
Orient Express eggplant
Russian banana potatoes
Butte potatoes
Zucchetta Rampicante AKA tromboncino summer squash

and I love scarlet runner beans for their versatility: red flowers attract humming birds, the youngest beans are eaten as green beans, and the older beans make good dry beans.

Like Dave said. Each has its own place. Even the fruiting vegetables like tomatoes ,eggplants, melons, squash etc have too great a variation to compare.

I always find it interesting how people always comment on the tomatoes not being a vegetable thing, when most vegetables aren't, all the fruiting vegetables are in the same boat :)

I only have 1 year to compare... but I loved the Table Queen Acorn Squash the best of all the squashes and will throw that one out into the ring.

Cherokee Purple and Sungold Tomatoes
Orangeglo Watermelon
Silver Queen Corn
Blue Lake Pole Beans

I grow other vegetables but no other favorite varieties come to mind at the moment.

I will add a few:
Carrot: Scarlet Nantes... sweet, as far as carrots go.
Tomato: Cuostralee... great taste, great production
Sungold...
Beets: Cylindra. We only eat pickled beets and these are great for slicing, even when over grown as they don't turn woody.
Garlic... no particular variety as to me they all taste the same when cooked.

You will be very wise to give special attention to answers that live in your region. That being said, I hope others who live in MY region will answer. It's always fun to try new things that have a fighting chance of success.

Tomatoes: Big Beef (for production), Black Krim (for big slice flavor) and Sungold.(for flavor and dehydrating), San Marzano for sauce.
Beans: Emerite and Rattlesnake
Cucumber: Marketmore
Okra: Emerald
Lettuce: Nevada (delicious and heat tolerant)
Carrots: Baltimore (yummy and BIG)
Cowpeas: Zipper Cream
Collards: Georgia
Kale: Red Russian

Golden Jubilee tomatoes are tops in my book. Sungold cherry tomatoes. And sweet potatoes grown from slips off a store bought sweet potato.

I'm in 8a, Hampton Roads, Virginia.

Beans - rattlesnake

Sweet Pepper - Flavorburst

Hot Pepper - big Jim

Eggplant - fairytale

Cuc's - marketmore

I started this thread because I'm always on a search to find new and even better vegetable varieties to try. Keep the suggestions coming!

pepperonchini peppers- Italian or Greek

ball summer squashes, I prefer the heirloom kinds over modern ones.

Nasturtiums, all colors- tasty leaves and flowers, the green seeds make great capers, and they are great companion and trap plants.

Juane Flamme tomato

Garlic, lots of different kinds of garlic, and only a couple of them really have names.

Other than that, it's always a new thing for me. I am forever trying new stuff. I've only been able to do serious gardening for a few years though, so I haven't really found much that are repeat planters or mainstay veggies yet.

I'm delighted with Wando Peas

I garden not far from NHBabs, the colder edge of zone 5. Last night we had a Confection kabocha squash from Johnny's. It was so sweet! Unfortunately, Johnny's is replacing it with a "better" variety. I also like Delicata for an easy winter squash for 2 people. I don't care too much for the butternut varieties except there's a Baker's Creek Long neck butternut that was an excellent keeper. Didn't have the great flavor of Confection but I would grow it again.

Favorite zucchini is Costata Romanesco, a striped variety. Productive and great flavor.

Any swiss chard after it gets cold in the fall.

We liked Provider Bush green beans until I started growing the filet varieties. Good production.

I agree with Sugar Snap. They might get 7' tall and production is great. I've tried other varieties and don't get the same production.

Tyee spinach planted as early as possible.

Gilfeather Turnip, nice flavor but I think it's really a white rutabaga.

Decided I like Hakurei turnips. Was surprised that they grew very well even though I hadn't thinned them probably. I had clusters of turnips.

I really liked Fedco's Fingerling sampler except for the blue potatoes. I thought our grandchildren would love them but we can't get past the blue color. And this is supposed to be a very nutritious variety!

Carmen for a frying pepper that usually turns red.

Bush beans: Savannah (Harris) & French Filet, both heavy yielders but FF had unmatched eating quality

Bell Pepper: Agree with rfarley1 on Flavorburst (Burpee), yields were un-freaking-believable, in a trial row of supposed "top-yielders", it out-shined quite easily.

Sauce Tomato: Big Mama, really great yields (I counted every tomato and I picked 88 from this one plant in 2013) and makes excellent sauce

Slicing/Canning Tomato: Old Virginia, may not be the tastiest heirloom in the world (in my opinion that is Brandywine) but it is a great size for canning and yields are amazing, I picked 101 off of one plant in 2013.

Corn: It is surprising to me that everyone is mentioning Silver Queen, for me Silver Queen is way too late to harvest before corn earworm gets going (despite timed Bt apps) and I just think the breeders have come a looooong way and there are some better varieties out there. My favorite is a bicolor called Trinity, extra early, pretty short to better withstand heavy winds and excellent eating quality.

Onion: Candy, which is a yellow, day-neutral onion, bulbs up huge and uniformly for me in dry spring/summers. Does not keep for ever, but is quite sweet, so this is to be expected.

Sungold tomatoes - delicious and disease resistant

Cherokee Purple tomatoes - totally delicious

Fish peppers - hot but not too hot and very pretty

Louisiana Purple Pod snap beans - highly productive through the whole summer

'Sungold' Tomatoes have been the one variety of vegetable that have made it into every vegetable garden since we first tried them. Best tasting tomato I've grown and rarely make it to the table, because of snacking in the garden.

'Gonzales' Cabbage - a miniature that takes up only 10" so I can fit 4 across in our 4ft wide raised bed. Easy to grow, the size of a softball and just enough for one large bowl of cole slaw. Just right for us. Very happy with this variety and growing it for the 2nd time this year.

'Ministro' Cucumber - out of the FEDCO catalog last year, wow. Cucumber after cucumber for a long time. No trouble at all. Last year was 1st year for this variety too, so hoping to repeat this success this season.

'Sugar Snap' Peas, a winner. Very sweet, healthy and productive. I like that they grow tall and I can use all the height of my trellis.

Another vote for "Sugar Snap" peas. I have also tried various short and tall snap pea versions, including "Super Sugar Snap". Sugar Snap" for the win.

I would add Sungold but we ate them until we were sick. Think cherries in "Witches of Eastwick". But I still grow them.