The feeling that results from a recent breakup can be labeled loneliness. It's an acute pain, a sort of panicked confusion from suddenly losing something you've gotten very used to having around. This is very different from the feeling that results from having been single for a long time, even though this could also be called loneliness. That is more of a dull pain, a longing for something different than what you are used to.
And of course, nobody is completely free from the many-tentacled clutches of loneliness. Even those in relationships are bound to feel a few of its pokes and prods - whether it's the acute lonely-whenever-they're-not-around agony of a new relationship, or the dull they're-probably-as-bored-with-me-as-I-am-with-them ennui of many longstanding relationships.
This is not a bad thing. I think it helps to deal with these feelings, knowing that everyone else is feeling them in one form or another. It also eliminates dangerous "OMG I just have to [insert affiliative activity] or I'll be lonely and depressed forever" thinking. It may take new form, but whatever happens, it'll still be there, swimming around in that chemical fishbowl of your brain that always returns to its baseline level of happiness eventually.
In related news, I have still been unsuccessful in finding anyone remotely interesting on internet dating sites. Although maybe there could be some "spark" (LOL!!!!) with this person:
Real winner there.
Update May 17: I'm reminded of this quote:
"I live in that solitude which is painful in youth, but delicious in the years of maturity."
-- Albert Einstein
In other words, even if I never find someone right for me, eventually I won't give a shit.