The IEEE spec for RS-232 is 50 feet. Obviously it goes further under many circumstances, but you take your chances - especially using pairs on a wire carrying other stuff.
RS-232 is kind of a crappy design for any comms beyond desktop distances, because it involves detecting unbalanced 10v signals. The voltage is either there or it's not, so it's not enhanced by good wire, and is very susceptible to noise. RS-485, as my good friend George expounds in the previous post, is balanced, and therefore will go great distances with properly balanced and gauged wire, regardless of noise.
In the US, Black Box is my fave vendor of cheap, reliable powered and non-powered serial line drivers. They use 2 balanced pair (Cat 5 is balanced, "jake" is not). These line drivers are actually RS-232 -> RS-485 converters. The non-powered drivers are really slick (about the size of a matchbox), however they draw their power from the CTS pin, so they will not work with an RS-232 interface that's not fully pinned.
An example of an RS-232 interface that's not fully pinned is a GAZ display. It has only RX and GD, so if you want to use a non-powered driver with a GAZ, you have to rig up a little kit box which uses a 9-volt battery to power the line driver. My esteemed colleague Ted Savage in Montreal has a nice design for this, and I have slapped a few together myself as well.
"Non-powered" is really a misnomer, they're actually bus-powered.
Using the non-powered drivers, you should have no trouble going a mile. Using the powered ones, you can get up to 10 miles. Once upon a time, during the America's Cup, I used a pair of powered Black Box line drivers to drive a matrix scoreboard in Coronado from a PC in downtown San Diego.
You can always use the powered versions, but they are much bigger (the size of 2 tennis balls) and of course require AC 120v power.
One more thing. The slower the interface speed, the farther your throughput will go. 19.2 will surely not go more than a hundred meters, even under ideal circumstances. 2400 may go 3 times that.