The size and shape of the glass can contribute to the enjoyment of drinking wine. Whether you need to spend a fortune on your glasses (which I tend to break a lot of when cleaning up) is another story altogether.
Generally speaking a glass with a long stem lets you swirl the wine more easily (swirling helps bring out the smells of the wine, which is very important to the tasting process). The long stem also keeps the heat of your hand away from the wine. (Of course, with the way I've been served some wines, you have to grasp the bowl of the glass firmly and often just to warm it up!) In order to capture the scents, its nice to have a glass that is more narrow at the top than the area below (in other words, a large bowl). In this way there is a larger surface area of wine in the bottom and the bouquet of the wine can get trapped by the narrowing of the glass. (Which reminds me how often I have to stop restaurant servers from filling my glass of wine--even in places where there is very nice stemware, many servers just don't know how to pour.)
Riedel produces (web site: http://www.riedelcrystal.co.at) an expensive line of glasses, none of which I own. Supposedly each glass (and there are different shapes for different types of wines) is designed to maximize taste and aroma by delivering the wine to the right part of the mouth, as well as being shaped properly to catch and concentrate the scents of the wine. How you may ask, can this be?
In terms of acidity, tannins, fruit flavors, aromatic components, and the like, different types of wine have different palate profiles. These are sensed by different parts of the tongue, nose and throat. Supposedly, wine glasses can be designed to channel the wine as you sip it to the parts of the mouth where you will get the optimal tasting experience. It is said that there is a different place in the mouth for each wine, hence the different shapes for the glasses, based on centuries-old concepts. But whether you really need five sets of wine glasses (or for some even one set of really expensive glasses) is left to your own sensibilities. A non-statistical, admittedly unscientific sample size of public postings tells me that some swear that these Riedel glasses make a large difference, especially after side-by-side tastings between Riedel and non-Riedel glasses, and others don't. Decide for yourself!
TheInternational Standards Organization (ISO) in the United Kingdom sets forth a design for a wine glass which can be inexpensive but very useful. They are smaller and less exciting than the fancy, expensive glasses, but are a lot cheaper to replace when smashed by host, guest or dishwasher. Many people find them to be perfectly adequate, however do admit to liking glasses with somewhat larger bowls. Personally, I like the latter, but haven't found it necessary to get really expensive stemware.
Wine drinking is an adventure. Think about it. If you had an especially good wine experience, was it just the wine? Or was it also the events surrounding the drinking of the wine? Two identical wines could seem different merely by the activities that surround its consumption. A romantic dinner? While the glass you use may or may not have an impact, I suggest that other peripheral items may be much more significant.
Washingglasses somehow has gotten controversial. Seems some people object to the dishwasher (and I've found some truth to this). Probably one should merely watch out (whether washing by hand or machine) about using too much soap or detergent which might leave a residue that will affect the wine.
Storing glasses is also something to think about. I tend to break them (no, not drunk, just clumsy the next day). The cost of expensive wine glasses is going to add up if you are ungraceful, so there may be the temptation to store them in the cardboard box that they probably came in. If you do this, wash to glasses before use. If the cardboard as gotten at all damp, it may get moldy and contribute off flavors to the glass and to the wine.