Ever since my warlock Bonescourge on Demon Soul picked up engineering, I have been in love with that profession. Why, do you ask?
The sheer versatility it grants you, of course! Let's face it, the other professions have a rising curve of items that you can use, so it's better to leave off leveling them until you are at the level of the items that you can equip.
In contrast, there's actually a decline on how useful engineering can be to a toon, which starts at each level cap that you can advance the profession. Level 5,10,20,35,50,65.....at each of these levels, you want to max out the profession in order to make the most use of the items you can get.
I'm not going to discuss the level 5-10 gap, since you probably wouldn't even visit a capitol city yet. However, at level 10, you can powerlevel engineering up to 150 which gives you access to three different goggles, the stats of which would normally not be gotten until the late 20's. You also have a limited time portable tank in the target dummy, which does what a tank is supposed to do, by attracting monsters and allowing you to dps without the mobs beating on you. You also have some AOE bombs, which probably do a lot more damage then you would be able to crank out at that level.
Moving on to level 20-34 (level 150-225 engineering). A few more goggles become available at this cap, though I've never made the Craftman's Monocle. Melee toons go with the Bright-Eye Goggles, casters go with Spellpower.
More AOE bombs, with Solid Dynamite and Goblin Land Mine being the top contenders.
And now, we start really getting into borrowing from other classes spells, with major cooldowns.
Resurrection - Goblin Jumper Cables
Combat pets (like hunter and warlock pets) - Reaper and Dragonling. Unfortunately, the Reaper does kinda suck, but every little bit of damage helps, and you can get most of the mats back when he self-destructs.
Vanish - Gnomish Cloaking Device. I've used this on my level 20 paladin to get past the elites in Winterspring Gorge, to get to the demon vendor who sells gromsblood and felcloth.
Paladin Bubble - If you've gotten a toon to level 30 and picked Gnomish Engineering, you could make the bubble belt for any class that can at least wear leather. Going up against an elite or doing some PvP? Extend your life by popping this when you get low on health.
Druid Root - Gnomish Net-o-Matic Projector could be useful by rooting 1 elite in place while you beat on the other one. Again, have a Gnomish Engineer make it for you.
Dash/Sprint - 2 boots, the Gnomish and Goblin Rocket Boots. I highly advise using the Gnomish ones, since the Goblin ones can explode permanently.
Perception (human racial talent) - Keep getting ganked by an annoying rogue or druid? Catseye Goggles will boost your ability to see stealthed toons, cutting their advantage decisively. The only problem is the lack of stats on the goggles, meaning that you'll be killed at least once before you think to put them on.
Slow Fall/Levitate - Parachute Cloak is a must for any non mage/priest engineer. Since it's ilvl 45, it will accept the +12 agility to cloak enchant, unlike any other cloak under level 35. With 20 agility on my cloak, I usually end up keeping this equipped until level 65, when you can max out engineering to 450, and get the tinkering parachute enchant. For casters, you can just put +50 armor on it, and that's fine too.
This is the first item that is able to take higher level enchants, but it's certainly not the last.