you could use GIMP. it's a completely free tool. (www.gimp.org)

here's a video on removing/inserting people using GIMP:
www.youtube.com/watch?v=q7EAvaHwGDg

Do you have Photoshop? If you do not and you want to do this yourself, be prepared to invest several hundred dollars in the software. There are numerous online tutorials on how to do this, which detail the process far better than I can in the limited space here. This is a good guide I found in a quick Google search:

http://psd.tutsplus.com/tutorials/photo-effects-tutorials/quick-tip-remove-a-person-from-a-photo-with-photoshop-cs5%E2%80%99s-content-aware-feature/

It's hard to do well, though.

The other option is to do it professionally, which personally I'd recommend. Any professional photo editing or retouching service will help you out. I'd recommend talking to a professional photographer you've worked with in the past for a recommendation (and often they're equipped to handle it themselves), but simply Googling "professional photo editing service" will yield a ton of possibilities. I'd go with the professional approach in this case, since it is an anniversary present.

Oh and one more thing. If you want a specific recommendation, I have a good friend who is a professional photographer and extraordinarily talented at this sort of thing. I don't want to anger the Woot gods and advertise for him here, but feel free to PM me sometime if you want me to pass along his info.

Not sure what he'd charge, but I doubt he'd be cheap.

Generally speaking, this isn't an easy thing to do, especially if you want it to look good.

@okham's comment had me thinking... if you had a print out of the photo that you can mess with, maybe it'll be easier to start by physically removing/covering the people by hand/markers/glue, scanning it, and going from there.

Depending on the background, cloning or masking would work. It could be done in GIMP as mentioned or Photoshop Elements and Paint Shop Pro. A (legal) copy of full blown Photoshop may be cost prohibitive unless you do this sort of thing all the time.
The biggest problem is people want a magic button to do things.
That being said, I have done this and wouldn't mind looking at one of the photos. No guarantees though.

The software Inpaint at http://www.theinpaint.com/ is made to do this specifically. There is a trial download at the site; I don't know if it is a limited (watermark, etc.) trial. It's twenty buckaroos, if the trial leaves their trademark on the picture but it looks like what you need.

You basically paint over the areas (faces) you want to remove, and it clones in an averaging of the surrounding data in the photo. In a lot of pictures, it works great; depends on the background. Go to the site and take a look at the demo video. Good luck!

I believe GIMP or a professional would be the best choice; for this occasion, I would personally choose a professional.

@tsfisch: I certainly see your point, but to present the other side: the people included in family wedding pictures are not necessarily the ones considered by the bride and groom to be "worthy" of being in the pictures; rather, who ends up in what picture can be a complicated calculus in blended families. I assume a "former stepparent" would be a stepparent who is no longer married to one's parent (for example, the bride's father's former wife, or the groom's mother's former husband). I can easily see a bride and groom being pressured to include their parents' then-current spouses in pictures and yet, years later, desiring a wedding photo without their parents' former spouses.

It all depends on what the background is around what you're removing. It's not super easy either way. Photoshop Elements for just over $100 might have the needed tools in it. Gimp is a little tougher to use, but free.

I've done hundreds of these. It can take hours per picture or just minutes, depending on what's around and would be behind the subject. I did once remove a house from a picture to show a mock-up of what it would look like torn down and replaced with a billboard. That took two days. And it still didn't look perfect.