Branch out. Buy stuff you've never tried. Cook it in a few different ways.
You like corn and you know that frozen corn that was boiled tastes different than corn on the cob and creamed corn. You know that some places make it quite oily and you know how you like that. Maybe you've had it roasted and know how that tastes.
ALL the veggies taste a little bit different depending on what you do with them. If someone doesn't like creamed corn, that doesn't mean they wouldn't like roasted corn on the cob.
You have to try them different ways. It takes time, but if you really want to get more veggies into your diet, invest some time!
Make Leek & Potato soup. See what you think. Roast some parsnip, squash and potato. Compare.
It is very likely that you'll find more veggies you like.
Baby carrots (baby anything,really) are better than regular - not carrots that are cut into shapes to look like baby carrots, lol, which are plentiful and easy to find...but real baby carrots are awesome.
Some more mature things are really good, too, like edamame.
Find recipes. Watch Alton Brown, if you get the Cooking Channel.
If you can, get a book like The Visual Food Encyclopedia - or just look up different veggies online, so you know what they are, what to look for when you buy them.
Go spend some time in the produce department.
There are SO MANY veggies and you already have some that you like. There will be more.
I was a "Corn, potatoes, green beans and carrots only" person, too, once upon a time. I tried new things and found some I really liked.