Quakeworld is probably the only game that fits the bill for me, I used to go into the uni computer labs late at night to play it online. I even travelled from home back to uni during the holidays in the daytime just to play it. Racked up some big phone bills, messed up my degree, and was probably fairly close to being addicted. I'd stay up all night playing and move to American servers if things were a bit quiet in Europe. At one point I was consistently clocking 30hrs+ a week and was ranked #1 in the world statistically (although I wasn't actually the best player in the world!). Over 10 years later and I still play it, albeit not to the same level.
Of course there were a few single player games prior to that such as Championship Manager '93 that took a chunk of my time, but not to that extent.