Everyone here is right, across their variety of opinions! I often create such sounds for real-world computer interfaces, as opposed to the software you see in films.
Tone generation is the key starting point. In my opinion, the secret sauce boils down to envelopes and filtering. I've designed sounds for UI's by taking nearly microscopic samples from field recordings and with some amplitude and filter envelopes, you'd think the Autechre Virus had hacked yer kernel. ;-)
I think that even tiniest bloop, bleep, squirk, and frrwwweee needs some "animation" to it, via envelopes, filtering, and/or automation. Reflect on the sound design of even Star Trek: The Next Generation series, now more than a decade ago - strong stuff for this very reason. The more pure the tone is, the more analog it sounds, which is fine if you're going for that kind of sound, but it can sound pretty dated against modern pictures.
In terms of source material, if you chop up a sample small enough, anything can be source material. (One of my most-reached-for UI sound libraries is my collection of DAT tape read errors!) If you're more of a synthesis kinda person, I'm +1 with Ian and Justin on knob-laden hardware synths...or, like my Waldorf Pulse+ analog synth or the Logic ES2 synth, any complex synth with a random patch can help unstick you, creatively. I've also found that the free audio utility Audacity has a number of handy tone generators. Short, transient sounds are great too - any sort of drum sample kit can be a good starting point if you're willing to push it far enough.