The answer in short, is "yes" it does matter. The origin of the shape of the glass can be cultural or traditional, but even these point to the ultimate goal of the glass, which is to highlight the nuances of the beauty of the wine and its bouquet.

A cabernet or merlot glass has wide bowl and narrorw top to funnel the fragrance upward to the nose. The roundness of the rim steers the wine to the front of the tongue where the sweetness can roll across and be detected. A pinot glass such as the one in your photo, has a short bowl from rim to stem top, to concentrate the more delicate aroma. Its wide bowl also allows for swirlling to release the tannins.

A chablis glass is narrow at the top forcing the wine to the front of the tongue to taste the subtle fruit melody. White wine does not need to aerate as red does, so the wide base is not required. A champagne glass is very narrow at the rim, making the bubbles continually move to the top so that you experience the fizz and subsequent fruitiness from the popping bubbles.

Upscale restaurants often train their wine stewards or sommeliers in the proper etiquette, cultural and technical aspects of wine service. If you are not sure which glass to use, most people consider the cabernet glass to be "the" all-purpose choice. However, if you have an opportunity to experience wine using the proper flute, you may find that yes, it does matter which glass is used.

This link is helpful when matching your wine with your glass:
http://www.bestwineglass.com/pages/wine_glass_guide/8.php

Most wine drinkers would agree that different styles of wines demand different types of wine glasses. At its most basic, think of the preferred wine glasses for Champagne and sparkling wines (a flute), red wines (a wine glass with a larger bowl) and white wines (a smaller bowl). This led to the development of the concept that close matching of the type of wine glass to the style of wine would be of benefit to the wine drinker, a concept which a number of manufacturers of wine glasses have grasped firmly with both hands. On such manufacturer is Riedel, an Austrian firm, that makes a huge range of wine glasses, of many different types, suited to every conceivable style of wine available. Personally I feel such a large range is overkill. I suspect most wine drinkers could quite adequately get by with just two or three different types of wine glasses. I would suggest as starting point the three types of wine glasses mentioned above - a standard glass for whites, something a little larger, perhaps, for reds, and of course a flute or similar style for Champagne or sparkling wine.

Wine Glasses for Reds:

The Bowl: Wider
The bigger flavors in reds need to spread out. The wider bowl also lets in more air, which releases bold aromas and flavors.

The Opening: Wider
Dip your nose into the wider bowl to get a load of more complex aromas.

Wine Glasses for Whites:

The Bowl: Narrower
The smaller capacity helps keep temperatures cool longer.

The Opening: Narrower
The lighter aromas waft well in a narrower glass.