Your wedding is about your love, being with family (if you so choose), and finding your own meaning and symbolism, and not necessarily about family politics, or showing off how much money you can spend on a one-day event. It may also help to think of the money you save as the down payment on buying a home to share, or some other shared goal. If there is something you want to spend a little more money on (e.g. one photographer friend who just got married didn't want to compromise on hiring a great photographer), sort that out now, too.
Have a "stage manager". I don't think I've ever seen this one in the guide books, so here's your "nontraditional" or "creative" idea. If you're being frugal, you're probably doing your own planning, but if you're having some sort of reception, especially a DIY reception, it's a really good idea to have someone who's not so closely connected to the event to help get things in order and do last minute errands (Didn't anybody get ice yet?). Ours volunteered, but you could hire someone you trust, as well. (In either case, be sure to thank the person with a nice dinner or other return favor.) If you do have attendants, it should help immensely to take the stress off of them.
Wear clothing that's not wedding-specific. You can go buy a dress and a suit just for the occasion, if you want to dress up, or go casual. Either way, get something you can wear again another day, for another event. You'll save a lot, and have something to show for it. You also won't be left with the question of where to store a fancy wedding dress for the rest of time.
Have few or no attendants. If you will have attendants, encourage them to wear clothing that's not specific to your wedding. Or, do something very simple to unify the theme, such as matched neckties and ribbons or scarves.
Consider casual. Think luau, beach party, barbecue, or picnic. You and the guests will all be able to relax and have fun, not fiddling with assigned seating, or worrying about spilling on fancy clothing. If your "dress code" calls for denim, Hawaiian shirts, or anything like that, be sure to let people know when you invite them.
Keep the guest list small. How many people are you going to be able to have meaningful conversations with in one day, anyway? Certainly not 200. Depending on how much you want to do, you could go with just a couple of witnesses, or immediate family only, or you could probably manage up to 50-60 people without a lot of expense, assuming you keep everything else pretty modest.
Have your guests take photos. Whether or not you also hire a professional photographer, spread the word that you'd like guests to take photos, and that you'd like copies. Sharing photos digitally is very easy, and should cost little or nothing. We handed our camera to one of the guests, as well. The guest we chose was a cousin's boyfriend who didn't really know who anyone was. I imagine it gave him something to do, as well as an opportunity to get to know his fellow guests.
Reconsider the rings. The rings, at least, you will be keeping, but plenty of rings are beautiful without breaking the bank. My fiancé and I got a pair of titanium rings on Etsy, choosing craftsmanship over cartels. Another option is to refurbish and resize a ring that is already in the family, if there is one. In any case, you may want to read up on where diamonds come from, before you buy one. There's nothing romantic about it.
Stay local, and choose a modest venue. You'll reduce travel expenses and expenses overall. Get married at home, at a relative's home, or at the local courthouse. Or, choose a nearby park, beach, historical home, or similar. Most such venues come at a fraction of the cost of a hotel or restaurant ballroom. Staying small will also help with choosing a modest venue.
Do your own cooking or have a meal catered by a local restaurant. If you have kept the guest list small, it's not that tough to do a barbecue for a couple dozen people, supplemented with a few different salads and side dishes that you can prep in advance. It will also be within your budget to take that many people out to a good, local restaurant.
Go easy on the liquor. Liquor is expensive, and the cost can add up fast. Keeping the overall quantity of liquor in check also lessens the chance of having drunk guests carrying on by the end of the evening.
Relax and have fun with it. This is a luxury that money can't buy. In fact, spending a lot of money on a wedding often has the reverse effect: when there is so much invested, there's lots at stake, and everyone is super self-conscious about making a mistake that could ruin what is supposed to be a perfect day.