More than 100,000 marriages are performed in Las Vegas every year. Blood tests are not required and there is no waiting period in the State of Nevada, so basically all you need to get married here is a valid driver's license, money($35) and a fiancé. After you visit the Clerk's office to obtain your marriage license, you have to find a chapel. Some of the casinos have chapels for more traditional weddings, but if you're going all the way you might want to consider the non-casino alternatives. Within a half-mile of the Strip between Sahara Ave. and downtown, there are numerous private chapels where you can get hitched.
The (very) basic chapel fee starts at around $50, and you should give the minister about $40. A variety of services are usually available including civil ceremonies, non-denominational ceremonies, ceremonies with original vows and marriages involving kids from previous relationships.

Where to apply for a marriage license:

County Clerk's Office
Courthouse - 200 South Third
Las Vegas, Nevada 89102
702-455-4415

The fee for a marriage license is $35.00.
The Clerk's office is open 24 hours Friday and Saturday, closes Sunday midnight and is open from 8 a.m. to midnight, Monday through Thursday. Identification is required to obtain a marriage license.

Partial guide to non-casino chapels:
(click for more info)

Chapel of the Bells
Chapel of Love
Cupid's Wedding Chapel
Graceland Wedding Chapel
Little Chapel of the Flowers
The Little White Chapel
Mission of the Bells
A Special Memory Wedding Chapel
San Francisco Sally's Victorian Chapel