I have had my birds trimmed from time to time - but for the most part I try to keep them full-flighted.  It's not an easy decision to make or to live with - and there are plenty of folks out there happy to shout at me for letting my birds keep their wings intact.

Before you clip your bird, please consider a few of these points:

1. I won't present myself as an "authority" on this, but in the nearly 30 years I've kept birds, I have noted that my birds appear to be happier, friendlier, and overall healthier if they are allowed flight.  If you want scientific evidence for why this is, it's out there (here's an excellent  science-based article on this subject).  For me, it's just enough seeing how my birds act.  They aren't as fearful or shy as birds who are clipped (I've known a few people who had clipped parrots).  Of course you can carry your clipped parrot around with you - but it's just so much more charming to have them be able to fly to you when they want.  In my experience, fully-flighted birds scream less, bite less, and are sick less often.
2. Parrots are beautiful.  Their wings are beautiful - and all the more so if their feathers are full.  Even a very light trim makes the feathers less lovely.
3. Trimming/clipping has to be done right, or the bird can become uncomfortable and may even start chewing and plucking it's own feathers out.  That's because feathers that are cut incorrectly can have sharp edges that poke them on the back and sides.  It doesn't feel natural and the bird instinctively tries to preen and correct it.  They end up self-mutilating because the sensation drives them bonkers.  Once a bird starts to self-mutilate (overpreening) it's very hard to stop them.
4. Cutting feathers is also a bit risky because you could hit a "blood feather".  If that happens, you've got a mess on your hands - and a potentially dangerous blood-loss situation for the bird.
5. Fully-flighted parrots can get into things that a clipped parrot wouldn't, that's true.  But I could not say that the clipped bird is per-se "safe".  A clipped bird isn't able to care for himself as effectively.  It can't fly from danger.
6. Clipping a bird doesn't stop it from flying (unless you pretty much rip out every feather).  Bird bodies are designed for flight - and it takes a surprisingly small amount of feathers on their wings to allow them to lift.  When you clip, you are not stopping that (unless, again, you've really mutilated them).  What you ARE doing is preventing them from being able to maneuver easily.
7. Worried about having "polly poo" all over the house?  I guess that's a legitimate concern - but you can potty train your bird.  There will still be the occasional accident, but bird droppings don't smell (if the bird is healthy) are easy to clean up (most of the time...).  And what kind of person would cut the legs off a dog because he poo'd in the house?

Although I am very strongly "pro-flight", I have had almost all of my birds trimmed at one point or another.  It wasn't an easy decision to make - but I considered it a temporary measure.  Here are my experiences with clipping:

1. Aussie is an excellent flier, and I'm very proud of him when he performs his daring aerial acrobatics.  But when he was about a year old, he suddenly developed an "attitude problem" and started flying at my face when he was angry with me. These "road rage" incidents seemed to happen when he'd been allowed to look into a mirror or other shiny surface for a while.  He'd gaze at his reflection and become quickly enamored - and violently jealous if anyone got too close.  Once he even flew right at me and nipped me on the lip (it bled a bit).  That was the point at which I knew I had to take action.  I did three things: I put him in a different cage, put the cage in a different place, and had the vet give him a light wing trim (just enough to slow him down a little). This triple-whammy worked, and overnight Aussie became (again) the sweet-spirited 'tiel that we have today.  When his wing feathers came back (in the next molt) he continued to behave well, and has been a good bird ever since.  Today he is fully-flighted again.
2. Bubba was about 2 years old when Pakshi came to live with us.  Bubba's natural curiousity and total lack of respect for other people's space led him to be continually flying over to Pakshi's cage and climbing all over it.  Pakshi ignored it at first, but then started to become enraged when the other birds were in his territory.  When Bubba flies, he makes a lot of noise (his wings sound like a tiny little motor or a huge bumble bee),and when he was out, I'd hear him lift off, but he was so fast I couldn't catch him before he'd get to Pakshi's cage.  I feared that Bubba was going to lose a foot, a beak, or more if this didn't stop.  So, as a desperate measure, I had Bubba's wings trimmed to slow him down a bit.  This didn't actually stop him, but it slowed him down enough so that I would have time to intervene.  He eventually lost interest in invading Pakshi's space - and he's been fully-flighted for the last 18 months.
3. Pakshi had been severely clipped before I adopted him.  He came to me never having known how to fly at all.  As he came into his first full molt and his flight feathers started coming in, I had quite a bad time with him.  He wanted so much to fly like the other birds.  You could just see the longing on his little face when Bubba or Aussie were out moving freely from cages to couch and back again.  Finally Pakshi started trying to fly - but his way to do it was to climb up on something and jump off (and then crash to the ground in a heap).  It was comical at first, but it became scary quickly because it he seemed to form the idea that if he just climbed high enough, he'd jump and have enough time to get the flapping going.  I started calling him "Evil Kneival" - and had to keep him close by when he was out.  Even with close supervision, he still managed to climb up too high and do heart-wrenching belly flops on the kitchen floor.  Twice he broke blood feathers in the process (but after crashing would turn around and start climbing right back up again).  Poor little guy - he was so determined.  Eventually, with enough time for the feathers to grow in (plus frequent "flap flap" training with me) he learned to fly.  He's never been as confident as the other birds, but he does well considering his bad start.  I believe the lesson here is that a bird should be allowed to learn to fly before he's clipped or trimmed.
4. Jesse came to us as an unweaned baby, and thankfully had not been trimmed or clipped.  I was very determined that I would not cut those lovely wings - and as Jesse grew stronger she began to experiment with flying.  It was amazing - it took her about 4 days to go from "no flying at all" to jumping off whatever she was sitting on and successfully navigating to sites as far as 40 feet away (even turning a corner partway in flight).  We were thrilled, of course, but that newly learned flying ability wasn't accompanied with graceful landing skills or the maturity to understand that certain surfaces are verboten.  We adjusted as best we could (all breakables removed from the bookshelves), but when her new confidence in flight led to an attitude problem (she suddenly started refusing "step up" and was acting generally "bratty") and when she began to develop the habit of flying to the family room curtain rod every time she could (forbidden territory for a host of reasons, not the least of which is the fact that the curtain rods are made of pine...)  I knew we had to take action.  We had the vet give her a trim.  Just like Aussie, she dropped the attitude immediately, and became more cooperative.  Now we're working on teaching her how to have fun in the "parrot approved places" (which actually includes most of the house).  She can still fly quite well, and can still get to the curtain rods, but she doesn't go there as much, and I think she's starting to understand that they are off-limits (the last time she climbed up there, I heard her make a noise that sounded like me saying "No, get off!").  Only time will tell, but we're hopeful that when she molts in the spring of 2006, we'll be able to leave her fully-flighted like the other birds.