Resistance to Digital converter
If you are familiar with microcontrollers then you can use an ADC. Place the unknown resistor as one half of a voltage divider (with known precision resistor), apply known voltage and measure the output at the junction. Do the math and you can work out the unknown resistance.   

There are a few variations on this (see Wheatstone bridge, pictured below) and you can get quite complex with it the more accurate you need it to be (see LCR meters also - they use a known frequency and measure amplitude and phase angle, so you can obtain a lot more data, e.g. DF, Q, &theta;, etc)

Wheatstone bridge configuration:



You can also get ICs and off the shelf modules that can be configured to measure voltage/current/resistance/etc. Obviously a multimeter (e.g. with USB/RS232 link) will do what you are asking for, but I'm guessing there must be a reason you want to avoid this route.