Because console connections use such low overhead and bandwidth, even aging 386s and 486s can be used. Linux makes an excellent and inexpensive remote console server. Just SSH into the box and access the serial ports from there. This is especially useful for dial-up connections. Keep in mind you don't need to use Linux here--we're just using it for our example. Other Unix and Unix-like operating systems, such as OpenBSD, would work fine. Just note that the naming convention of serial ports under different versions of Unix may vary slightly.
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