Data and Tasha Yar.
And yes, Kirk's greatest love was The Enterprise.
From The Naked Time:
KIRK: I've got it, the disease. Love. You're better off without it, and I'm better off without mine. This vessel, I give, she takes. She won't permit me my life. I've got to live hers.
KIRK: I have a beautiful yeoman. Have you noticed her, Mister Spock? You're allowed to notice her. The Captain's not permitted
SPOCK: Jim, there is an intermix formula.
KIRK: Now I know why it's called she.
SPOCK: It's never been tested. It's a theoretical relationship between time and antimatter.
KIRK: Flesh woman to touch, to hold. A beach to walk on. A few days, no braid on my shoulder.
KIRK: Scotty, help.
SPOCK: Stand by to intermix. I'll call the formulae in from the Bridge.
UHURA [OC]: Entering upper stratosphere, Captain. Skin temperature now twenty one hundred seventy degrees.
KIRK: I've got to hang on. Tell them. Clear the corridors, the turbo lift. Hurry. (Scott and Spock leave) Never lose you. Never.