In my house there is what is called the "Two Bite Club", they have to try two bites of EVERYTHING on their plate, and if they still don't like it, then just keep introducing it to them once a month or every couple months.

Make it fun, of course!  If your child is involved in food choices, preparation, etc., he'll be much more likely to taste them.  Try taking him with you when you shop, and let him choose something to buy and try, if he's interested.  Just raising his awareness of what veggies are out there will eventually make a difference.  It's true that many children need to be exposed 15 or more times before they're willing to try a new food - so keep exposing him.  Don't force him to try anything, but encourage him to.
   Another way to get children interested enough to try their veggies is to grow some of your own.  When children help with any part of the growing process, and watch plants flower, then fruit, and see the process, they are often very excited to taste the resulting veggie - preferably right out of the garden!  I run a home childcare, and my 3 - 5 year olds beg to taste the squash flowers, green beans, fennel, asparagus, etc., that they help me to grow.  Having the option to taste, and the power to make that decision, are very powerful motivators to young children.
   Preschoolers love to help, and to be involved!  Your child can help wash fruits and veggies, cut them (with a butter knife and lots of supervision), put them in the pot to cook, etc.  Again, when I make veggie soup with the children, they want to taste all the ingredients, including raw beets!  Many fruits and veggies can be sliced thinly (adult's job) and then children can use small cookie cutters to create attractive shapes to nibble.  Cucumbers, watermelon and cantaloupe all cut easily enough for children to create shapes - and if you have alphabet cookie cutters, they can punch out their name in veggies.  
   Try offering raw veggies with a fun dip option.  Peanut butter is very tasty with carrot sticks and apple slices.  Ranch dip goes well with many veggies, and may be enough to motivate your child to try them.  Try hummus dip (make it together, or store bought), cream cheese stuffed into celery sticks, or other familiar tastes coupled with a new veggie to add appeal.
   An excellent book on this theme to read with your child is I Will Never, Not Ever, Eat a Tomato, by Lauren Child.  There is even a tv take off, Charlie and Lola.  Lola is a VERY picky eater, but by making trying new foods fun, Charlie helps her learn to try them.
   Happy tasting to you and your child!