Do you know, I wondered how this thread was going to go, but its great that you've left it as subjective as it should be when it comes to opinion - not "what is the best", but "what is your favourite"!
Its really interesting to hear what it is about different mods that really inspire different people.
As for me, I find it hard to pin down just one, but I actually think Tinker's Construct might well be it.
I discovered TiCon before the advent of the mega-crossbows (which are fine, in my opinion) which many people label "OP"; when I first found it, it was a little-known mod that was part of the Hexxit modpack, and I just... LOVED it. Building your own weapons, making improved materials, pouring molten metal out into casts?! It was AWESOME. I loved the look of it, the functionality, the progression, everything. And I feel like TiCon2 is an excellent sequel, so I will include that too - the wonderful "cooling" visuals on the metals, the added functionality with touching tables, the wide variety of material traits - its a great iteration on a great idea!
Honourable mentions go to: SGCraft, Chisel, Chisels & Bits, Thaumcraft (all versions!) and Immersive Engineering. Also Actually Additions (LOVE those item models!), Redpower2, and the original Applied Energistics (for the spatial storage, holy crap!!!). And Thermal Expansion - all versions, right from the start!