user220: Stepper motors are often pricey for a large motor. However, with a powerful, standard DC motor and a rotary encoder, you can "simulate" a stepper motor. How accurate are rotary encoders with Arduino just with a basic loop and not much other code? Is it going to "miss a pulse" and not record enough rotation often? How can I handle this with much more code? Is there a better way to do this? Would interrupts help? Is there some sort of circuit that would help with this problem?
Note: It will probably not exceed 4 rotations a second... (That may be a lot but if you're doing a lead screw type mechanism that would only be 24 inches a minute if there is 10 rotations per inch of linear motion.)

user973: Adding some references to already-written libraries and examples, to enable comparison between different approaches, and experiences with speed versus susceptibility to missing steps.
Reading rotary encoders:
http://playground.arduino.cc/Main/RotaryEncoders
Quadrature Encoder too Fast for Arduino (with Solution): http://www.hessmer.org/blog/2011/01/30/quadrature-encoder-too-fast-for-arduino/
Teensy Encoder library: https://www.pjrc.com/teensy/td_libs_Encoder.html
Reading rotary encoder on Arduino:
http://www.circuitsathome.com/mcu/reading-rotary-encoder-on-arduino/

user407: Interrupts are what you would use in this situation.
The rates that you have mentioned are slow enough where you probably would be able to count it inside of a loop, however this is not recommended, as a typical loop will take many clock cycles to complete, and depending on the number of instuctiuons per loop, you may miss some counts.
Interrupts are made for this purpose, as they can be triggered at any time, regardless of the state of the loop.
There is a function named attachInterrupt() which will take three arguments.

Interrupt Pin
Interrupt Service Routine
Mode

Below is an example for counting an interrupt
volatile int myCounter = 0;

void setup(){
    attachInterrupt(0, count, RISING);
}

void count(){
    myCounter++;
}

The Modes are as follows:

LOW, CHANGE, RISING, FALLING

More information about using interrupts can be found here.
Depending on the encoder you use, you will need to tailor the code your needs, and do some more calculations to determine your position, but this should be a good starting point.
Edit
Here is some example code from Arduino Sandbox for using a rotary encoder.

220: <p>Stepper motors are often pricey for a large motor. However, with a powerful, standard DC motor and a rotary encoder, you can "simulate" a stepper motor. <strong>How accurate are rotary encoders with Arduino just with a basic loop and not much other code?</strong> Is it going to "miss a pulse" and not record enough rotation often? How can I handle this with much more code? Is there a better way to do this? Would interrupts help? Is there some sort of circuit that would help with this problem?</p>

<p>Note: It will probably not exceed 4 rotations a second... <em>(That may be a lot but if you're doing a lead screw type mechanism that would only be 24 inches a minute if there is 10 rotations per inch of linear motion.)</em></p>
 973: <p>Adding some references to already-written libraries and examples, to enable comparison between different approaches, and experiences with speed versus susceptibility to missing steps.</p>

<p>Reading rotary encoders:
<a href="http://playground.arduino.cc/Main/RotaryEncoders" rel="nofollow">http://playground.arduino.cc/Main/RotaryEncoders</a></p>

<p>Quadrature Encoder too Fast for Arduino (with Solution): <a href="http://www.hessmer.org/blog/2011/01/30/quadrature-encoder-too-fast-for-arduino/" rel="nofollow">http://www.hessmer.org/blog/2011/01/30/quadrature-encoder-too-fast-for-arduino/</a></p>

<p>Teensy Encoder library: <a href="https://www.pjrc.com/teensy/td_libs_Encoder.html" rel="nofollow">https://www.pjrc.com/teensy/td_libs_Encoder.html</a></p>

<p>Reading rotary encoder on Arduino:
<a href="http://www.circuitsathome.com/mcu/reading-rotary-encoder-on-arduino/" rel="nofollow">http://www.circuitsathome.com/mcu/reading-rotary-encoder-on-arduino/</a></p>
 407: <p>Interrupts are what you would use in this situation.</p>

<p>The rates that you have mentioned are slow enough where you <em>probably</em> would be able to count it inside of a loop, however this is not recommended, as a typical loop will take many clock cycles to complete, and depending on the number of instuctiuons per loop, you may miss some counts.</p>

<p>Interrupts are made for this purpose, as they can be triggered at any time, regardless of the state of the loop.</p>

<p>There is a function named <code>attachInterrupt()</code> which will take three arguments.</p>

<ol>
<li>Interrupt Pin</li>
<li>Interrupt Service Routine</li>
<li>Mode</li>
</ol>

<p>Below is an example for counting an interrupt</p>

<pre><code>volatile int myCounter = 0;

void setup(){
    attachInterrupt(0, count, RISING);
}

void count(){
    myCounter++;
}
</code></pre>

<p>The Modes are as follows:</p>

<blockquote>
  <p>LOW, CHANGE, RISING, FALLING</p>
</blockquote>

<p>More information about using interrupts can be found <a href="http://arduino.cc/en/Reference/attachInterrupt#.UxVGrvldXvM">here</a>.</p>

<p>Depending on the encoder you use, you will need to tailor the code your needs, and do some more calculations to determine your position, but this should be a good starting point.</p>

<p><strong>Edit</strong>
<a href="http://playground.arduino.cc/Main/RotaryEncoders#.UxVIwvldU4J">Here</a> is some example code from Arduino Sandbox for using a rotary encoder.</p>
