Death knights were designed to be the anti-caster class. Blizzard had initially envisioned death knights to fill the niche role of tanking caster bosses and gave them abilities that are excellent against casters such as Anti-Magic Shell and Anti-Magic Zone. They also have abilities such as Strangulate (1 Blood Rune, 2-minute cooldown) and Mind Freeze (20 Runic Power, 10-second cooldown) which can silence and lock-out casters from particular schools. They won't hesitate to use Strangulate and often use it early in the fight in order to gain the upper hand. On a good note, death knights have a particular weakness that can be exploited by smarter players...
Aside from their ability to pull opponents and ensnare them, death knights have no natural way to remove snares. This makes them particularly vulnerable to kiting. They have no rush abilities such as a warrior's Intercept or fast-moving forms like a druid or shaman, so a slowed or snared death knight is vulnerable to ranged attacks. In PvP, death knights are often in Unholy Presence, which grants them improved mobility by 15% (as well as reduces the global cooldowns of all their abilities by 0.5 seconds). Death knights won't hesitate to use Anti-Magic Shell to shake off magical snares, but have nothing against physical snares such as Hamstring or poison effects such as Crippling Poison. This is one of their few pitfalls, and classes able to take advantage of this should find it a little easier to deal with death knights. Remember, however, that Death Coil is a ranged attack, so make sure to kite them when their Runic Power is low.
Unlike last week's druids, identifying a death knight's spec isn't as simple as checking out their forms. However, unholy death knights are very easy to spot by virtue of the swirling bones around them and their having a permanent ghoul by their side. Those ghouls are named, too, as opposed to the generic type summoned by other death knights. Blood and frost-specced death knights are a little less obvious so it might take actual engagement to reveal their specs.
While death knight abilities seem formidable, not all specs have access to all their fearsome abilities. For example, a frost-specced death knight with access to Hungering Cold, arguably the best peeling ability in the game, won't be able to summon a gargoyle. An unholy-specced death knight -- a popular tree for PvP -- isn't likely to have the self-healing capabilities of a death knight specced deep into blood. An opponent that spawns Bloodworms with her strikes is likely to be deep in blood and won't have the deeper frost and unholy abilities. So on and so forth. What's important about identifying specs, as is true with all classes, is that it gives you an idea of what to expect.
It won't be easy to identify a blood-specced death knight right away. The most telling sign, perhaps, would be the Bloodworms that usually spawn when they start attacking. They will almost never use Dancing Rune Weapon unless their opponents are vulnerable and are at low health, so don't expect to see that ability until very late into the fight (hopefully never). Blood-specced death knights are a good counter against melee classes, as they can pop Mark of Blood against an opponent to heal themselves. They will usually do this against fast-hitting opponents such as rogues or Enhancement shamans. If you're a melee class and find yourself with a Mark of Blood, try to remove it or disengage until the duration of the debuff wears off. Barring that, turn off auto-attack and only use hard-hitting attacks. Smarter death knights will even apply Mark of Blood on pets, who have low damage but fast attacks. If you see the debuff on your pet, turn off its attack.
Blood-specced death knights can recover a lot of health in a very short time. They can activate Vampiric Blood and use Improved Rune Tap (1 Blood Rune) while spamming Death Strike (1 Unholy and 1 Frost Rune) to generate massive health very quickly. Because the blood spec doesn't rely on pets, some death knights will even Raise Dead and immediately follow it with a Death Pact in order to heal. The most you can do in this situation is to remove diseases because Death Strike will not heal at all if no diseases are on the target. Also remember that those low-health Bloodworms help heal the death knight, so eliminating them with a well-placed AoE should help you in that fight.
While blood-specced death knights have incredible durability and self-healing capabilities, they aren't known for dealing as much damage as the other two specs. Diseases won't be particularly strong and they won't have a ghoul to occasionally stun and pester. Fighting blood death knights is all about trying to keep their self-heals under control, so healing debuffs or Mortal Strike effects work particularly well here.
Frost death knights aren't easy to spot, either, but can sometimes be identifiable through dual-wielding and opening with an Icy Touch. Some will have the Chilblains talent, which should appear as a snare debuff, and this should tip you off. The surest but unfortunately most painful sign, of course, is when they finally unleash Howling Blast on you. One interesting point about frost-specced death knights is that they are more likely to use their Runic Power on Frost Strike rather than a weaker Death Coil, so try to kite them as much as possible.
Save your trinket for Hungering Cold, which they will pull off in order to escape or maneuver. They will try to deal as much damage as possible by using Obliterate and Howling Blast, which is a dangerous thing especially if Rime procs. Casters in particular should be wary of frost death knights, who might even pick up Acclimation, a deep Frost talent that boosts resistance to particular schools of magic. They are also able to cast Mind Freeze for free, essentially capable of interrupting spellcasting every 10 seconds without worrying about Runic Power.
Also noteworthy is that a lot of frost damage bypasses armor because, well, it's Frost and not Physical. This makes frost death knights pretty effective against other melee classes, especially considering they can also mitigate physical damage with Unbreakable Armor. Note that when death knights use Lichborne, they are considered undead and can therefore be Shackled or Turned. They are also able to heal themselves (a Runic Power intensive endeavor) using Death Coil.