That schematic you linked to has a mistake - the inverter on RXD is hooked up backwards.
The 7404 is just an inverter. RS232 uses both inverted levels and different voltages than TTL. The 7404 takes care of the levels, but the MAX232 will take care of the voltages as well, producing the -12 and +12 levels needed by rs232.
There is a version of RS232 that will operate on 0V/+5V. This circuit _could_ work depending on the particular serial port you connect to.
There is also a game you can play with some transistors and "steal" the RS232 levels from the device you're interfacing with (see http://www.arduino.cc/en/Main/ArduinoBoardSerialSingleSided
). This is cheap and usually works, but I have had occasional problems with that method.
To have some thing that will work well, get the MAX232. There are other devices that do the same thing, but the MAX232 is the most common. The MAX233 will let you dispense with the capacitors, but it costs a lot more than the MAX232.