In our modern society, artificial intelligence is creeping into everyday life - automated music/movie recommendations - Google's self-driving car, everything from the Roomba automatic vacuum to the Mars rovers. It's a part of basic life these days - thus it makes sense that they would be included in any sort of Sci-Fi story. That said, widespread high-grade AI tends to be detrimental to the usual goals of RPG - if computers can be better than humans, why are we even here? One of the classic themes in literature is the triumph of the human spirit - it goes against some of our basic drives when machines are better than us.
So how to reconcile the seemingly inevitable march of AI that we see all around us?
1.) An easy answer is just make AI's optional player-characters - Androids or PC's that live entirely within computers - Shadowrun has options for this, as do a number of other RPGs. Usually this means you need to put some sort of limitations on them, otherwise things get overpowered. How awesome would the Enterprise be if the whole crew was made of Data-like androids? (I'm assuming post 1st season Data, after he was a bit more human-like.) In this context, we're allowing AI's to BECOME human-like, and thus it's OK that Data is waaay stronger and smarter than the rest of us, since now he's human after going through a spiritual journey to have human emotions and feelings.
2.) War with the AI-driven machines that now necessitates laws against AI. For example, Eclipse-Phase, Dune, and Battlestar Galactica universes all had cataclysmic battles with AI-gone-rogue. There's probably dozens of other examples from the Sci-Fi world. However, I wanted to avoid any kind of post-apocalyptic world - it's been done many times before, and done better than I could ever do it.
3.) Practical limits to AI - In Shadowrun, a Rigger's drones have smart-dog level intelligence They can be given simple commands like 'Guard this place' or 'Attack this target' - but cannot do much more than that. Autopilot has a similar limit - usually the rules are designed so that the best autopilots can only approach the competency level of a 'real' player-character. Within Interstellar Profiteer, I've very intentionally ruled that computers CANNOT make SLIPP-drive jumps, thus preventing automated shipments from dominating the market. As it turns-out, this isn't as an original idea as I thought. Andromeda - the sci-fi show developed from Gene Roddenberry's notes has a similar limitation, as does Diaspora (embarrassingly enough, both universes call their FTL a slip-stream. A little close for comfort to SLIPP-drive). This is the option I'm going with for my universe.
Other examples of dealing with the AI problem? Throw a comment in there!