I use boning and fillet knives most often when preparing meat, and a slicer knife when portioning it after cooking - heck, I use my kitchen shears more often than my chef's knife when prepping raw meats (especially poultry and fish).
The chef's knife is used to prepare veggies, which is where the bulk of any cuisine's prep is, vegetarian or not. It's designed to reduce aromatics like onions, carrots, peppers and celery into minced, diced or cubed pot-ready ingredients. You can get through almost any food prep task with a chef's knife, a paring knife and a bread knife.
If you like collecting and playing with fine knives in the kitchen (and that's as fine a hobby as any), there are some fruit and vegetable-specific knives you could benefit from trying out.
- Nakiri and Usubo - these are the knives used by japanese chefs expressly to prep vegetables. The nakiri is a more robust everyday knife, the usobo is meant for making exceptionally thin cuts. They are meant to chop rather than slice.
- Tomato knife - This is a serrated knife used to cut soft and fragile food, such as tomatoes or ripe peaches. It's thinner and more weildy than a bread knife, and a good accompaniment to thicker European chef's knife styles.
- Bird's Beak - This is used to tournee root vegetables, pare round fruit, and to make delicate and tricky garnish cuts.