Let me start with some coarse (over)generalizations, and then mention a few bits of trivia, then close with a disclaimer.
The modern definition of unemployed is "having looked for work recently". I'm not entirely sure that definition is appropriate for Rome. Modern Western Liberal Democracy is organized around the notion that "companies" provide employment, and that people seek employment. Unemployment results in a dramatic decline in economic and social status.
Although there were workshops in Rome, and there were teams that organized to perform tasks that no individual could, I'm not aware of anything that resembles the modern limited liability corporation. Roman politics and economics were based more on relationships than on companies. Romans belonged to a family, and to a tribe, and usually to some kind of patron/client relationship. Depending on their social class, they may have also belonged to one or more social organizations (e.g. burial society). If someone wanted to work, they would rely on these connections to find them employment. "Unemployment" didn't really result in the kind of economic and social decline we find today because these social bonds provided a safety net. If for some reason you were isolated from your social network, that might be a definition similar to "unemployed", but there were mechanisms (adoption, social organizations, etc.) that made the social networks fairly resilient.
As @edn13 points out, the proletariat lived off the dole. There was no real reason for them to look for work.
I believe, although I can't check right now that the Aristocracy never worked; I believe the notion that work was unbecoming to the Aristocrat reaches back as far as Ancient Rome. Although they were never employed, they couldn't be unemployed because they would never seek work. (Obligatory exception: The Aristocracy was obliged to engage in public service, including a number of civic offices).
Tradesmen looked for work, but they weren't unemployed, they were just tradesmen looking for work. Technically, the self-employed can never be unemployed, it is just that their business is going through a slow spell.
Slaves never looked for work. Many were employed to perform tasks that were mere displays of wealth - for example some were chained to the doors of houses to act as gatekeepers.
Slavery also prevented unemployment in a different way; if for any reason your economic status declined precipitously, you could sell a relative, or ultimately yourself into slavery. You probably only wanted to do this if you had a marketable skill.
The ultimate bottom rung of the ladder was to be sold to a latifundum - a farm. I haven't researched these very much, but my impression is that a slave on a latifundum may be the only historical example that is more horrifying than American chattel slavery.
Disclaimer - I'm well aware that these are coarse, unsourced generalizations, and I'll be dissapointed if certain people don't vote this answer down for my hypocrisy; they are correct to do so. I think the other answers are good, but I thought the question would benefit from a brief analysis of the underlying assumptions.