It can be healthy, but it depends. Eating a hamburger is very different from eating lean poultry or fish (avoid fish with a high mercury content). High calorie foods are fine, of course, but you should be choosing foods that are nutrient-rich, not just high in fat. Prenatal vitamins should help cover all the bases, so abstaining from or limiting meat intake shouldn't be a concern as long as you are eating a wide variety of protein-rich and fortified foods (nuts, beans, mock meats, eggs, dairy, legumes, fortified breads, pastas, and so on...). If you are vigilant about your diet, you can be a healthy mum-to-be either way. :)
If you do decide to eat meat during pregnancy, you might scout out your local farmers' market. That way, you'll be able to learn about the source of the meat and its content (hormones, antibiotics, etc.) directly.