I know I'm coming to this late, in part because I've been thinking about it. I have discovered that I like structured learning. I left university in 1998, and in 2000 I took my first Open University course. I love to learn, and it's very good in keeping my mind occupied (when I'm not learning, I tend towards getting a little obssessive, or over-thinking unimportant things, or writing ludicrously long repies on a forum, and so on). I could learn stuff on my own, but I like having the guidance of what to learn and the objective measure of coursework and an exam result.
Because my OU sutff is studying for 'no reason', I so far have about half a humanities degree, plus an undergrad certificate in astronomy and planetary science. I'm a bit random, easily distracted in to another subject area, but that's the joy of it. And it's of no consequence at all if I give it up for a year or ten, or if I fail the exam, etc.
I thought very seriously about taking the OU's music course. I knew that I hadn't done music for a long time, so I'd need to get my theory up to speed and remember how to find my way around a keyboard. This led to me taking G3 theory a few years ago (I can't remember off the top of my head, though at least I do actually have the certificate for this one at home - 2003?). My intention was to be at G5 by the time the course started.
In the end, I didn't take the OU course - because it has a one-week residential school, it is one of the more expensive courses. I decided that I couldn't afford it, and in any case the residential school idea was giving me panics before I'd even booked the course. While I could get medically excused form the residential school if I really needed to (panic disorder/agoraphobia), I'd still have to pay the full course cost - and I just didn't have the money. So, I didn't take any more theory exams, as I no longer "needed" them.
January 2007, re-discovery of music via my recorders. I'm loving just being surrounded by music, even if I'm not playing. Quite often I'm sitting at work, doing work on one screen with a pdf of a bit of music on my other screen - just read the music, think about the fingerings, etc (I get a lot of time sitting around just watching as things compile/import/export - I make good use of it!)
I've re-devoured my AB guides to music theory (which I bought when contemplating the grade exams prior to the OU course). I'm tempted to do G4 in the summer, because, well, why not? It's fun

I really enjoy the challenge of having something specific to work for that will be marked. If I just had to learn for me, then I could skip the difficult bits. I mean, why would I ever need to know how to compose a rhythm carrying on from a double-dotted quaver? When I clap rhythms, I'm OK to quaver level, and sometimes get a bit lost with semi-quavers (I have to tell myself instead of '1-and-2-and' it's '1-an-an-an-2-and' etc!). Add dots to quavers and I'm easily bemused

But that doesn't matter, I don't need to play anything with double-dotted anythings in. And a rhythm to words, well, I'd just make it out of crotchets, quavers and minims, if I had to make one at all. I'm not a songwriter, I don't need that skill

But, if you do an exam, you have to do the difficult bits as well as the easy bits. And so you learn the hard parts, and they become easier, or they make sense, and it adds to overall musical ability in some way (e.g. if I see something with double-dotted quavers in, I may become able to hear the rhythm in my head, rather than having to hear somebody else play it first.)
For practical exams, it's more difficult. I'd probably enjoy taking practical exams just as much as I do the theory exams and the OU work. I can teach myself pieces, and have the CDs to know what something is 'supposed' to sound like - the technical, music-playing part of an exam really doesn't bother me at all.
The real problem for me - and I know this is completely silly - is the people-side of it. I'd need an accompanist, where do I find one of those? OK, there are websites, I can email an accompanist, find out prices, etc, before I commit to anything. Or would I be better with a teacher; I'm sure I would, just to make sure I'm playing 'right', that I'm aiming myself at the right level, and so on. And to make sure that I'm not going to completely humiliate myself on the day by actually playing dreadfully for the level I'd entered myself at! But there's finding a teacher, contacting them, finding out if I like them, how much do they cost, how often do they think I need lessons, do they do AB exams or do they use 'the other lot' (and does that matter to me, and if so why?), etc.
All this paragraph is really an excuse, it's the "phoning a stranger" part that's scary

Would the teacher think I'm silly, would my husband think I'm silly, I'll tell you what, I'll just play for myself at home and at my local SRP...
The pleasure of playing is what I want from music - the joy of music itself. While I may learn better in a structured setting, of which exams are undoubtedly a significant part, at the moment I'm happier doing that for myself (I can do G2 descant scales now!)
So, um, I should have a conclusion after all of that, shouldn't I? What do I / would I get out of exams - a defined level of achievement, a structure to my learning that I enjoy and could otherwise be missing, and the challenge of working on the difficult bits that it's very easy to skip when you just do-it-yourself.