Sometimes my 3 year old won't try something as yummy as a donut because it's not something I've offered to him before and he does not think it will taste good. Obviously that is not a food I'll keep trying to get him to taste. But by offering healthy foods on several occasions and letting your toddler get used to the idea of trying something new, you can be successful.
Just remember this simple rule: it's the parents' job to offer healthy foods and it is the child's job to choose if he'll eat it and how much of it he'll eat. This can help you avoid food battles that can become more about "power" struggles than nutrition.