I occasionally rinse with water. The residual water definitely changes the flavor and texture of the next wine. This may not always be a negative (I have seen a bit of water bring out flavors of Scotch and Bourbon, so why not wine?), but I'm sure it more often than not does detract from the wine. As already mentioned, the water is not purely neutral, but there are often trace minerals and chemicals in the water which can alter the taste, and the water does significantly dilute the next wine. But the previous wine that was in the glass can also change the flavor of the next wine. So what to do?
One option would be to rinse with water, then season, then take the full pour--and do these steps repeatedly for every wine. At a large tasting, this obviously becomes cumbersome to the point of impossible, so I try to judge what wines would be similar, and go consecutively through a flight without rinsing. Rinse (or hydrate, as mentioned by g-man), then season the glass with the first of the new flight.
Sometimes rinsing is mandatory, especially in the case of a corked or just plain awful wine (remember I frequently taste Michigan wines
), and also in the case of a bunch of sediment in my glass. If it doesn't look like I will get a chance to have my glass seasoned, I will try to dry the inside with a napkin, but that has it's downside, too.
If I'm just drinking for pleasure with friends, I will always just take a small pour of the new wine first to swirl around, before taking the full pour. Sometimes that little blended sip can be quite interesting, too!