The answer is generally, yes, you probably do need to supplement the light coming into your window in order to grow light-loving vegetable plants.

Testing light in my window with a foot candle light meter. Good light, but not enough of it long enough.
If these plants are going to be nutrient packed enough to be worth your while growing them and investing all this time, you should give them the light they need to photosynthesize and process the nutrients you are feeding them.

Lots of stem on this leggy arugula plant
Plants that do not get enough light grow “leggy”– they are all stems and the leaves look like they are perpetually reaching out for mooooore liiiiiiiiiight pleeeeeeease. Even my South facing unobstructed windows are not really getting enough light this winter and my arugula is getting looooooooong in the leaves.
Most of the information on lights we have been working with comes from the rather prolific specifications in
Gardening Indoors with Soil and Hydroponics by George F. Van Patten.
Windowfarms Light Policy
We have decided to use CFLs (and LEDs soon, as they become more affordable) because the big grow lights used in greenhouses and by pot farmers are simply not viable to live with in city apartments and frankly just use too much electricity.
Instead the windowfarms project has been focused on making the most efficient possible use of consumer grade CFLs. We are not using just any old CFLs. We have found the ones that are only recently available on the market most likely to grow vegetable plants through all stages of their lifecycle.
Lighting for plant growth is a complicated science and I will not burden you with understanding anything more than the fact that 4 factors are important for growing with CFLs under these conditions:
1) The Kelvin color temperature of the lights- The color of light produced by the sun changes over the course of the year and plants are tuned into these changes. Light color triggers them to enter different stages of growth, so we want to be careful about light color. Consumer brands use lots of different names like soft white, bright white, daylight, full spectrum. Don’t go by the term alone. Find out the color temperature (marked with a K). We have been using 6500 K bulbs and have produced healthy flowers and fruits in several species. Between the natural light coming in your windows and the artificial light, we’ve probably got a pretty good spectrum.
2) Wattage- This boils down to the strength of the lights. We want them to be strong. Thus far, we have produced good results using 27 Watt actual/100 Watt incandescent equivalent bulbs. We may find that we can go down to 75 watt equivalents (19 actual watts) or below depending on the array and proximity. This needs to be tested!
3) Proximity to plant- Van Patten claims, ”
Light from CFLs fades fast and must be placed close to plants. The bulb produces very little heat and can be mounted about 2 inches(5 cm) away from foliage to achieve best results.” So, we have tried to make the lighting moveable so that as plants grow, they are always within this distance from the bulb. We add in fishing wire as trellicing so that we can movethe branches if they try to grow too close to the light and start burning themselves (Plant thinks- yay! i have fnally arrived at the sun. Ouch!! It’s hot!).
4) Duration at each life stage- Just like teen humans need more sleep, adolescent plants need more light than adult plants do. Think about how plants are young in the spring when the days are longer and then the days get shorter again in the fall during harvest season. We use timers to control the lights, sometimes leaving the lights on longer than the sun is out. For more, read Van Patten’s Photoperiod section on page 88. You need to learn a little bit about the kind of plants you are growing and their natural best growing conditions, which you will then mimic with your setup.
Here are the specs on the bulbs we use. We have been using them because they are available all over the country at Home Depot and they fit our requirements. However, please feel free to find similar brands and post them here for others. 
Blue package marked 100 Watt at Home Depot
N:Vision brand
SKU 599-526
27 Watts (Package says equivalent to a 100 Watt incandescent bulb)
Kelvin color temperature= 6500K (according to customer support) but marked 5500 K
120 V 60Hz 0.450 A
Supposedly these are available with globe covers but I have never found them. That would be rad because it would keep plants from singeing themselves.