No sudden rush of love for me but I'm not a very emotional person so I wasn't expecting it. I had a fairly uncomplicated induction, eight hours in all during daytime, with an epidural, so I wasn't too knackered, just run-of-the-mill tired after giving birth.
I had felt her slide down the birth canal, like a fish with shoulders, arms and legs, which was very surreal, and then they briefly took her to the other end of the room to prep her and give her a cursory wipe. After that they put her on my chest and I thought that she didn't look too bad and that I had made her and all that. However, at some point after I delivered the placenta and I was stitched, I was given the choice of either having her taken away and delivered at the room, properly washed and all, or keeping her and we would both be wheeled back to my room, at which point I said my baby was staying with me. Like I was going to let go of her.
And that was it, really, I've never let her go since. You don't need to get the big rush of love/hormones/whatever to prove that you're worthy or something. If you get it, it must be such an amazing feeling, but everyone is different and there's no right or wrong. In my case, I then went on to spend the next night getting up to feed her with the worst butt-pain ever (I believe that I had dislocated my coccyx during delivery, days/weeks later a got a couple of crunch-crunch moments when it apparently snapped back in its right position) and I just sort of cuddled and talked to her through it, so yes, you can very much love your baby and not get the famous rush.