You may be tempted to have a cash bar for a variety of reasons, from cutting costs on your already swollen wedding budget to wanting to avoid having your guests overindulge before having to travel home from your wedding. And while this is understandable, there are more acceptable options than asking for your guests to pay for their beverages at your wedding.
If you can't afford an open bar, but want to serve alcohol at your wedding, stick to just beer and wine. Beer and wine can be dramatically less than cocktails, and as they have often have less alcohol content, your guests won't be as likely to be too sloshed to drive.
If you can't afford an alcohol tab at all, serve non-alcoholic beverages. Granted, you might still get a few grumblings (which is their faux pas, not yours), but there are plenty of adorable ideas. Serve an assortment of ice teas, Italian sodas, or lemonades from giant glass jars and pitchers.
Ultimately, your wedding is a party. Asking your guests to pay for their drinks would be akin to having a bbq and charging them for a beer. Have a wedding that welcomes and hosts your guests well, and also stays within your means.