Children love eating with their fingers, and touch is important if they're going to learn to like certain foods, so try chopping up carrots and cucumber into sticks for them to munch on, maybe even with sauce for dipping.
Vegetables come in all shapes and colours, so use this to your advantage to get them to eat their greens (and yellows, oranges, reds, etc). Go for brightly-coloured mixtures, and get them involved in the preparation too.
Vegetable soups, tarts, gratins and bakes are a really good way of incorporating veg into your child's diet.