Lots of good responses so far, though I think you can ask a hundred people and get 107 different responses (some of them biblical!). The first challenge we have is that English has only one word for this range of experiences. Greek has four. I suspect other languages may have even more.
I'd like to propose something...
That "warm lovey-dovey gushy romantic feeling" IS love.
Before anyone asks the mods to ban me, let me explain... this feeling is
not all that love is, by a long shot. It is part of the wealth of experience which God has given to us in relationships. It is the bait on the hook, the cherry on the sundae, the appetizer at the feast. It passes with familiarity or with tension, but may be renewed (even frequently). It gets us "in the door" of relating beyond mere friendship or acquaintance. The problem is that we are easily deceived into believing that this feeling is all that love is, which is incorrect and naive. So when the feeling passes, we mistakenly think the relationship is in trouble, or not worth the effort to continue.
This feeling doesn't develop in certain relationships, but only in romantic (or potentially romantic) ones. It is the crazy glue that holds people together long enough for other parts of love to grow. It is the solvent which temporarily breaks down walls, goes around defenses, and undermines barricades so that deeper love may enter. It makes the difference between that special one and all the other family and friends whom you "love". It is what makes us
feel special to another. It doesn't exist in our relationship with God (there are parallels though); this is a gift from God unique to human relationships.
Clearly, there is much more to love... but I won't bore you all by sharing the entire February 14th sermon!