Engineering is indeed a viable (if still largely unprofitable) profession.

The basics

    Dynamite and Bombs: They come in many forms, from these ultra-cheap versions to sophisticated gadgets. But no matter what type you make, they fulfill two important functions: they're wonderful ways to level engineering, and they provide a ranged attack/pull for a class that is otherwise lacking one. (Unless you grab Avenger's Shield or Holy Shock, but those are only available at later levels.)
Seaforium Charges: Tired of those pesky rogues complaining about ret DPS and "losing their spots?" Make sure they really lose their spots by taking away one of their most vital roles. These formerly less-than-useful charges can now open chests as well as doors. Surprise your group by opening chests -- or really emulate a rogue and just take things for yourself after the group disbands. (Note: Do not do this.)

    Transporters: It's like having an extra hearthstone -- and we all know how paladins need those! These transporters can take you to Gadgetzan and Toshley's Station (for Gnomish Engineers) or Everlook and Area 52 (Goblins). However, it can also transform you into another race, make you an "evil twin" or "good twin", or strand you on an island in the sky. Use at your own risk.

    Target Dummies: Yet another thing pallies lack at low levels is a viable form of crowd control, and unless you're a protadin, you might find handling pulls of 3+ mobs difficult. Target dummies can keep some of your opponents occupied while you burn down their companions. You can also get Fused Wiring from their corpses.

    Repair Bots: These raid-savers let everyone repair their weapons and armor and sell off trash so you can ... undergo three more hours of wipes and re-blessings. On second thought, you might want to leave these at home.

    Flying Machines: Okay, it's not paladin-specific, but a lot of people have picked up engineering just to make these super cool mounts. If you're going to go to 350 for your goggles, why not push it all the way for this ... individualistic machine?

What to wear

    Early Goggles: Sure, they're cloth, but their lack of a level requirement means they're super-helpful at lower levels, when there are no headpieces around -- much less headpieces with stats.
Goblin Rocket Launcher/Gnomish Poultryizer: At first, it looks like just another fun-but-semi-useless engineering trinket -- the goblin version does damage and stuns your target, but also knocks you down for two seconds, and the gnomish thing makes ... chickens. . But a couple of things make this good for pallies. It's a decent long-range puller for retadins and other pallies without pulls. And the 45 stamina is nothing to laugh at. The rocket launcher is far superior to the poultryizer, though.

    Force Reactive Disk: Let's be honest -- you're not going to make this shield unless you can find someone with the (Molten Core drop) pattern. Nevertheless, it's an excellent situational piece for a protadin who's trying to hold aggro on a ton of rampaging mobs, as long as you can withstand the 50% chance for 1 point durability loss on a successful block. Plus, the light show is apparently fantastic.
Furious Gizmatic Goggles/Justicebringer 2000 Specs/Tankatronic Goggles: One of the best reasons for paladins to take engineering. With the right amount of mats (and three Primal Nether), you can make excellent epic helms for all three paladin specs. The Tankatronic Goggles' raw stamina and mitigation will last you until Illidan, the Furious helms will make up for all the ret gear that your guild is giving to DPS warriors, and the Justicebringers are about equal to Tier 5 (although they might be the weakest of the goggle options, just because there's lots of other great healing plate out there.)

PvPness

    Gnomish Mind Control Cap/Goblin Rocket Helmet: These hats rock for low-level PvP fun, but fizzle against targets higher than 60. The Goblin helmet, like most goblin things, lets you rocket around and run into someone, stunning them for 30 seconds. The much more evil Gnome version can only be used out of combat, but allows you the chance to mind control your opponent. You can run them off a cliff, under the sea, into an instance, etc. The Goblin helmet is especially useful for low-level twinks because of its 15 stamina.

    Recombobulators: These trinkets will dispel Polymorph on another player, making them great for arena matches against mages -- that is, if they can actually be used in arenas. No one seems to know for sure.

    Rocket Boots Xtreme: Flag running. Arenas. Annoying the person chased you. Is there anything these can't be used for? Admittedly, they'll probably still use a druid, but you can say you tried.
Reflectors: Hard to find and only intermittently useful, these things can be caster-killers if they're not resisted. Particularly nice for making three-minutes mages one-shot themselves.

    Nigh Invulnerability Belt: Okay, this one is probably going to get you reported for "ZOMG he's bubbling twice in a row!" But it'll be worth it, especially if they wind up blowing all their long-cooldown,
Mana-expensive moves against your invulnerable shield.

Making some cash

    Of course, getting all the way to 375 isn't going to be cheap. Engineering isn't exactly renowned as a cash-producing profession, but there are a couple of items which sell well. The Khorium Toolbox has a great guide which we previously covered here. Gyrochronatoms, Mithril Casings and Adamantite Frames are quest items for both factions. Deadly Blunderbusses are a good money-earner for the Horde, while Advanced Target Dummies are required to complete the Magram Centaur quest line in Desolace. The Zapthrottle Mote Extractor can help you gather those necessary Primals, and there's usually a market for Adamantite Shells and Stingers.