I've used Nikon's 70-300mm VR lens for dragonfly, damselfly and butterfly shots. It has a minimum focus distance of about 1.5 meters, which works fairly well for most dragonflies and butterflies due to their large size. Getting much closer than that tends to scare dragonflies and butterflies off, but it can be done if you are patient. Extension tubes do help to get closer with smaller insects (bees, etc) - I never tried extension tubes with the Nikon, as you lose autofocus, particularly when using Nikon brand extension tubes which are manual focus only).
I now mostly use Canon and currently use a Canon 180mm macro lens for most close-up and insect shots. It is roughly equivalent to the Nikon 200mm (which I've tried) and both have a minimum focus distance of about .5 meters. For close-up and insect shots, I've tried various combinations of teleconverters and extension tubes with the Canon 180, 300 and 400mm lenses, but usually prefer the bare lenses as they focus faster and gives better detail. A teleconverter does not change the minimum focus distance, but it does increase the size of the image in the frame. By the way, you cannot use a Nikon brand teleconverter with a Nikon 200mm macro lens - they aren't compatible. You could conceivably use a Kenko TC with that lens, but I wouldn't recommend purchasing one for close-up work if you didn't already own one.
I also use 100mm (and shorter) macro lenses for some shots. If the subject allows a close approach, shorter lenses work well, especially when used with a flash. I've seen excellent macro galleries by photographers who use the 100mm macro exclusively - so that might be another option.