The following things have really been bugging my Dark Angels:
1. Heldrake with Baleflamer. I can stay in my Rhinos, in which case I can't shoot properly and my Devastators die, or I can disembark, in which case it Vector Strikes, killing 2 or 3, and the Flames the remnants, killing a huge number. As an AV12 Flyer, it's very difficult to put down.
Speaking as a CSM player, the Heldrake is a godsend for us. As one of the toughest fliers in the game and with a respectable damage output (tailored to killing MEQ), it's a great investment in points for us and a great way to soak up enemy firepower... and distract the enemy from shooting at our more fragile assault units.
Its "downside" is that it only has a moderate damage output. Okay, it really builds up over the turns, but it's not like many other fliers, with multiple large blast template missiles and
about 4 other guns. You can ignore it if you don't want to devote the sizeable points chunk of your army that will be necessary to reliably take it out.
What to do about it if you want to kill it? Uh, ally in Imperial Guard in order to get a Vendetta/Hydra? Spend ~275 points on Devastators w/ flakk and a ADL with quad gun/icarus lascannon? There are few real easy counters, unfortunately. Or, from my point of view, I guess, fortunately. A Vendetta and a squad of devastators with flakk might be your best bet.
2. 20 Cultists. Autoguns and a Heavy Stubber, sat in a piece of 4+ cover. I cannot apply enough firepower or get close enough to charge. They shrug off the scant firepower I send their way and 9 times out of 10, capture an objective.
One word: flamers. Or any templates that ignore cover, really--can DAs get Thunderfire Cannons? Alternatively, a combat squad of marines who charge them should be able to take them out, provided the Overwatch isn't that bad. Yeah, these involve getting close, which you say you're having trouble with. Could you make a flamer-Ravenwing squad, or something? Zoom in, torch most of them, then charge the survivors and mop em up...
Flamer Special Weapon Squad in a Chimera (or the aforementioned Vendetta!), if you're going the Guard alies route, should be able to mop em up with relative ease. Just don't disembark until you've killed most of them and don't attract the notion of some bigger chaos unit--wait a few turns until making a beeline for the cultists, when his nasty units are committed elsewhere, or something.
3. CSM with Mark of Slaanesh and Icon of Excess. They almost ignore boltguns, and 1/3 of Plasma shots you send their way come off the invulnerable (added to 1/3 missing, that's a large decrease in firepower). In combat, they strike before Tacticals and with more punch.
Ummm, ally in Grey Knights with a Vindicare in order to snipe out the Icon Bearer? Hit 'em with a S8 AP3 battle cannon, somehow? (Vindicator, allied IG Russ). Meltas, if they hit, are basically an auto-kill.
Alternatively, and more realistically, tie them up with terminators. Their piddly I5 attacks will bounce off while your power fists will pulp them and you can laugh at the notion of "Feel No Pain".
4. 3 Nurgle Obliterators in seperate squads. Very difficult to get rid of before they kill a Terminator squad or expensive vehicle.
Also very expensive--228 for those three models, who are essentially a lascannon and a plasma cannon every other turn, or some other decent stuff at close range. I'd say ignore 'em and focus on the important enemy squads first. You're probably gonna take some casualties from ignoring them, but that's all right.
If you have plasma in the area that doesn't have anything better to fire at, go ahead and wipe one of the Oblits off the map. Otherwise--not to high a priority, I think. They're tough but only put out a moderate amount of BS4 firepower--If I were playing against that, I'd be fine with living with that while I killed his scoring units and designated assault units.
5. Daemon Prince with Sigil of Corruption, Wings, and Mark of Tzeentch. Flying with a 3+ Invulnerable re-rolling 1s is pretty damn tough. Today it charged a squad of Deathwing, before being charged by another squad. It ate both squads at the cost of 3 wounds.
First off, that Prince is illegal. The Sigil of Corruption is in the Special Issue Wargear section, and the Prince can only buy items in the Rewards and Artifacts sections. He can have a 4++ rerolling 1s, or he can have 3+ cover save evading with Nurgle--but only one of 'em.
Bolter fire, bolter fire and bolter fire. That combo certainly sounds nasty, but hey, you can't reroll rerolls. Force enough saves and he's going to fail some.
Use small units/skyfire units first, until you've knocked him out of the sky, then just let loose with massed bolter salvoes. If you have to sacrifice a small squad to bait the enemy Prince out of cover, it's a noble sacrifice, but worth it--then you can shred him with massed shooting. Make him feel the pain of that mere T5.
Also, a Librarian has a chance
of taking him out. With Biomancy powers (Iron Arm, Warp Time) or Telepathy's Invisibility, there's a good chance he'll survive the Prince's first smash attack and have a chance to strike back with his force weapon. Still, that's something of a maaassive gamble, seeing as more likely than not, the Librarian will just get torn limb from limb. Still, they make me catch my breath whenever my Prince has to face off against one in a challenge.
Edit: Spanner's got some great advice as well, and it's more tailored to the DA specifically. Listen to that wise man.