There really is no reason to have a date at a wedding. Presumably you will know at least a few other people there, and if the bride and groom do their job right, you'll be seated with them. So meet new people and have fun! You never know who you're going to meet (as DZGirl just attested
).
If your wedding invitation doesn't say "and guest", you do not get to bring a date or twist the bride's and groom's arms to invite someone for you to have on your arm. Weddings are expensive enough as it is! However, both members of a married, engaged, or living-together couple should be invited.