Fedora 16 may be installed on most "modern" x86 processors. (There are some "secondary architectures" supported by special interest groups for processors like Power PC, System/390 and ARM).
The minimum processor speed depends on the end use, the method of installation, and the specific hardware. Although some configurations might work on a Pentium 3, most users should consider a Pentium 4 or more modern processor, or the equivalent processor from other manufacturers. Fedora 16 is able to take full advantage of modern, multi-core architectures.