Super Street Fighter IV Arcade Edition has been out for a while now, and the one thing that everybody can agree on is that Yun is fucking bullshit. This guy is a character so overpowered that we can't chalk it up to anything but bad design: he's got an answer for every situation, a rush that can't be put down, and does huge combo damage for every jab he lands. In Guilty Gear he might be a normal character. In SF4 he is just bad news for competition. The scene's pretty unhappy: I had the pleasure of listening to Seth Killian play "Street Fighter Information Minister" on stream at a recent major tourney as Daigo's Yun effortlessly destroyed top players who usually give him some trouble.
Now you're seeing Yun (and his lesser brother Yang) a lot online, but the game's still new and the average guy who picks these characters doesn't really know how to use them. This will probably change as the game ages a little bit. As for myself, I tend to play Juri. Here's what I do against Yun when I see him, even though I've only fought four or five genuinely good Yuns online.
Generally speaking, you want to keep him out. Normally I try to be more aggressive with Juri, but if you get Yun in on you you're already in the process of losing. It's just like how you never want to be standing close to Zangief and blocking. You stand to lose much more than you stand to gain.
The first thing I do at the start of a round versus Yun is hop straight up into the air. This is, in my experience, the safest place to be against him. You'll avoid most of his go-to openers this way, and if he does his dash punch under you, you might be able to land with Hard Kick (which hits on both sides and continue with a combo. In fact, jumping straight up repeatedly at a safe distance is exactly how I deal with Yun's overpowered (get hit and it's a free combo, block it and Yun gets to rush you freely) EX dash punch.
And I hop, and I hop. If Yun does his palm attack-- he will: it's mostly safe, has a monster invisible hitbox, stays active for much longer than it appears to, charges meter fast, and does unreasonable damage-- you can time Juri's dive kicks to beat it. However, as I said before, the palm stays active much longer than you'd expect and the window to punish it is tiny. You'll have to work out the timing.
Once you've got Yun down he has an invincible and very safe wakeup (the jump kick special): best to bait it out.
Other than those openings, I just try to keep Yun out. Throwing fireballs at him is kind of a tough proposition, because of the way Juri's charge/release mechanic works. If you simply charge and throw a fireball, Yun has so much time to get in on you, and he will do so. The charge kick will actually beat Yun's dash punch if it intercepts Yun's dash, but it's not something you can do on reaction: if it happens you were just lucky and got out of a mistake. At mid-range I'll poke around with long-range hits like standing Medium Punch/Kick and try to stuff his advance, starting with those hop kicks.
I use Feng Shui Engine (Ultra 1) just so I can get in on him for free. This is a universal tip, but if you knock a guy down and use FSE, a fireball interrupted with FADC (focus attack dash cancel) will give you a free mixup as the opponent blocks the fireball. Yun can't use his invincible anti-air to get out of your string of attacks in FSE mode either, so you actually have a ten-second shot at the same damage opportunities that Yun has all the time. Good luck.
If Yun's in on you, just worry about escaping. An EX pinwheel kick will work as always, but considering it's your sole option there's nothing more obvious and telegraphed. If you have three bars at this point, EX pinwheel, FADC away if it's blocked, and count yourself lucky. It's very hard to pull yourself out of Yun's grasp. Just stay out, okay?