Alchemy's definitely a solid choice for every character class. Being able to make your own flasks for raiding, be they Stoneblood or Endless Rage, will always be a plus, especially if you have an herb source. You'll be able to stock Crazy Alchemist Potions and Runic Healing Potions for emergencies. In addition, Alchemy does have trinkets that can be useful for the 5-man and beginning raider levels of play. The Mighty Alchemist Stone is a nice companion to the Mirror of Truth if you don't need hit rating, while the Indestructible Alchemist Stone makes a fine companion for the Essence of Gossamer if you don't need defense.
The downside to all these trinkets is that they're imminently replacable. As you can see above, the Mirror of Truth and the Essence of Gossamer are already more or less equivalent to the alchemy trinkets, especially if you don't find yourself using the potion bonus much. You may find that you need to swap out your alchemist trinkets for needed defense or hit rating as implied above. Of course, you'll still have the potions and flasks. If nothing else, that's a good amount of money saved. And hey, there's always selling potions, flasks, and transmutes to other players, not to mention Mixology.
Blacksmithing and Death Knights, in theory, go together like peanut butter and jelly. We wear plate armor and swing big whomping weapons, Blacksmithing makes plate armor and big whomping weapons. If you decide to bring your blacksmithing up before you start in on your Northrend leveling, the profession provides some very nice leveling sets. Cobalt, Tempered Saronite and Daunting armor will singlehandedly make sub-80 instance tanking possible, and you can even start in on the Reinforced Cobalt and Savage Saronite armor if you want to get a head start on PvP gear. In addition, you'll be able to make some of the best pre-raid level 80 armor and weaponry in the the Spiked Titansteel Treads and Helm and the Titansteel Destroyer. Finally, you'll be able to churn out Eternal Belt Buckles.
Of course, the problem with the above is that most Wrath-era blacksmithing armor and weapons are BoE. So even if you're not a Blacksmith, it should be relatively easy to find them on the auction house or find a smith to make them for you. That said, there's still a major reason to stick with Blacksmithing: extra sockets on the Bracer and Gloves. Two extra sockets means you have more stats, more flexibility in achieving a meta-gem requirement, and that extra edge of power over a similar tank or DPS without Blacksmithing. Plus, you can sell the above mentioned BoE items for a decent chunk of change.
There's just not much here worth getting. If you have your heart set on making leather armor for your guild or leather-wearing alts, I suppose you could go for it, though. As long as you're crazy enough to do that, you can at least get the slight cheaper versions of the tanking and DPS leg enchants. You can also get the Attack Power and Stamina fur linings on your bracers.
But really, the enchants aren't good enough to be the only reason to take Leatherworking. Sure, you can make money selling some of the BoE armor and the BoE leg enchants, but you can sell BoE things from other tradeskills like Blacksmithing and Inscription and make things for yourself if you want to take that route. It's probably best to skip this tradeskill and just get the only slightly worse BoE versions of those armor enhancements.
This is another one that just isn't going to have more for the aspiring tradeskiller Death Knight. If you're absolutely crazy for bag space, you might take this one just so you can make your own bags. You can also get the Swordguard Embroidery, which is admittedly the best cloak enchant you'll find for a DPS Death Knight since haste isn't really our forte.
But really, unless you have your heart set on a Flying Carpet, there are more useful tradeskills you can take as a Death Knight.
Enchanting is certainly a nice convenient tradeskill to have. It's not as useful to us as some since we have Runeforging, but the convenience of being able to enchant the rest of your gear nearly at will is probably reward enough. Being able to stick Stamina or Assault on your rings is a good bonus as well. If you've been meaning to make one of your characters an enchanter, your Death Knight is probably as good a choice as any.
Jewelcrafting definitely has its perks. You can make a few pretty awesome BoE jewelry pieces that you can wear or sell. You can also cut gems for own slots and sell excess cut gems for a pretty penny, depending on the cut. There's also a series of trinkets, which, much like alchemist stones, aren't really the best in slot, but make a decent fill in until you get the good ones. Plus, these ones have gem slots.
Then, of course, there's the Dragon's Eyes. Bold Dragon's Eyes are just the thing for DPS, while tanks will like the stamina boost from Solid Dragon's Eyes. Rigid Dragon's Eyes will help you fill out hit rating requirements, and Thick Dragon's Eyes will make it that much easier to hit the defense cap. There's even Mystic Dragon's Eyes for the PvPers. They're also prismatic, which means they count for metagem requirements, meaning you have to use fewer superfluous gems to fill the requirement.
Overall, it's hard to go wrong with Jewelcrafting. For extra awesomeness, combine the extra gem slots of Blacksmithing with the Dragon's Eye power of Jewelcrafting. Of course, If you take this route you'll either need to level a miner or spend mucho moola on the AH to keep yourself supplied, but in this case, it may just be worth it.
Inscription is definitely a lucrative tradeskill. It will probably get less lucrative in 3.1, since dual specs will mean that people won't need to completely respec so often, and therefore won't need a completely new set of glyphs, but I imagine you'll still do OK cash flow wise. The big reason for this would be the Darkmoon Decks. Since Inscriptionists can make the cards, it means you'll find getting that Noble's Deck a lot cheaper for yourself and find that you'll have a steady cash flow when you put the cards you don't need up for auction.
That's hardly the only reason to take Inscription though. The various Inscription shoulder enchants do, in fact, stand head and shoulders above their Sons of Hodir equivalents. And when 3.1 hits, everyone who's anyone is going to want a Rituals of the New Moon. So if you're following the crowd and getting the new tradeskill with the new class, you'll have a couple very good reasons to do so.
It seems like Engineers are the most vocally dissatisfied with their tradeskill at the moment, but I have to say, I don't think they're that bad off. Yes, a lot of the old novelty and fun trinkets no longer work past level 70 and/or haven't been upgraded in Wrath, but what they have is pretty nice and solid.
Goggles continue to be the height of headgear fashion, and you can still get some pretty passable ones for both tanking and DPS. In addition, the agility flexweave underlay is probably a pretty decent tanking cloak enchant if you don't need the defense enchant. Beyond that, you can get some pretty decent utility out the Scrapbots and MOLL-E, and the Sonic Booster is a pretty decent stop-gap trinket until you get better. There's a bunch of glove enchantments, but even I have to admit that I'm not sure they're really worth using. But hey, finger rockets are least some pretty fun novelty. And while there's no Northrend teleportation devices, the old world and Outland ones are still useful for old world achievement chasing. And hey, those flying machines are still pretty sweet, if you can stand the engine noise.
There's probably not a right way to choose your profession, although if there's an optimal combination, it's probably Blacksmithing and Jewelcrafting, assuming you can afford to get your gems and ore from another source. As far as wrong professions to choose... Well, Tailoring and Leatherworking would come pretty close, but hey, whatever lights your fire. Either way, you have a long way to go to, so head out to Elwynn or Silvermoon and start picking those flowers, mining that copper, or whatever it is you're going to need. Good luck, Death Knight.