There is something to be said for "looking the part." When you are covering an event as a videographer it doesn't hurt to look like one. This also sets you apart and could help to distinguish you from an amateur with a camcorder. You are the pro there to get the shots. This may not work at a wedding, but for a sporting event it could be a must.
First it may convey to onlookers that you are a pro. Second it could open some doors otherwise closed to you. But there are other practical uses for this "look."
Wearing a photo vest gives you plenty of pockets to put lenses, backup batteries, extra tapes or cards, and the always needed cleaning kits. You may even want to have your company logo embroidered on it.
A photo vest need not be expensive. You can get one here (B&H Photo) for 30 bucks. Lightweight vests like this are comfortable in both summer & winter. Rather than dragging around a camera bag or (God forbid) leaving your stuff back in the car, you can have most of what you need right on your person so you can get to it quick. Even if you are just a hobbyist, it is still convenient to have all your accessories handy.
Sometimes you want people to know who you are. You want to advertise your company or services. When doing the job you need to wear the hat. Well, maybe a cap. Do you have caps for yourself or crew? It's easy to get a cap with your logo on it these days. You can have a few made at cafepress.com. Just upload your logo and buy them online.
You can have your logo or simply "Video Crew" emblazoned on the cap to signify that you are there to cover the event. You are the official videographer. This too can get you in places you may not otherwise have access to.
Golf shirts are also a good way to convey your company or videographer status. They are professional looking, sharp and comfortable. T-Shirts are comfortable but probably not appropriate for a business image. Give them to your customers, wear the sharp stuff yourself.
The way you present yourself in a video situation can be the difference between you and the other guy. This is not to say you should put on airs, but convey a professional image. If its a video for a blog or personal web site it may not matter, you are being yourself. But if you are representing a company, looking good is always a plus. It will make an impression on those who watch you perform your craft. That too can lead to more jobs.
Plumbers, electricians, pastors, police officers and firefighters all look like their job. There is no reason you cannot look like a videographer, after all that is what you are.