It really depends on the relationship.

There are some where I've felt sadness but also a great sense of relief/relaxation. Where I've known the relationship wasn't good, and while there was some sadness for hurt feelings, there was also a chance to breathe more easily.

With my most recent, it was a challenge. He gave me that bullshit, "it's not you, it's me." line, but there also was never an opportunity for us to have any time apart (physically, yes, but not entirely). Due to various things happening in our lives, we needed to be talking regularly as of about two days after breaking up. There was about a month or so of profound sadness, of my heart skipping a beat every time I heard that text tone, every time I got a message on Hangouts, of seeing his name pop up on Facebook and Twitter, and really, just a sense of being out of place/an emptiness whenever I went to our regular haunts, and where he lives (which is a couple of blocks or so from my work).