Okay, I'm not going to look this up, and I haven't built a circuit in way too long...but I believe the answer is NAND. IIRC, you can cascade NAND gates to implement any other logic, and they are very simple to build, so low-grade electronics often use them exclusively.
Please correct me if I'm wrong. Also, I've seen logic designers for windows; does anyone know of any for linux? All this talk has gotten me in the mood to geek out with circuits again.
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NAND is simple to build. If you short its two inputs together, you get NOT. Any gate can be made by a combination of NANDs and NOTs.