Without seeing the lightning, can you tell how far away it struck by how the thunder sounds? Is there any way to tell how far away a lightning strike is by how its thunder sounds? I thought one way might be by using the fact that higher frequencies travel faster than lower frequencies. Would you have to correct for the fact that thunder may not take a straight path? (If so, this would affect the distance calculation based on the time between lightning and thunder as well.)
 A: I presume you did not see the flash, so cannot use that as a timing mark.  From  Wikipedia "The dependence on frequency and pressure are normally insignificant in practical applications. In dry air, the speed of sound increases by about 0.1 m/s as the frequency rises from 10 Hz to 100 Hz. For audible frequencies above 100 Hz it is relatively constant. "  You might try to use the fact that high frequencies are attenuated more than low frequencies, but that seems very dependent on the terrain.
A: This is an interesting question.  Unfortunately, the answer is probably no for two reasons.  There is a nice way of telling how far away a lightning strike was by counting the seconds before the thunder reaches you though.  First let me tell you why your method probably won't work, then I'll tell you how to calculate the distance based on the time of arrival (a method which you might already know).

Why your method won't work without sensitive equipment.

*

*The phenomenon you are trying to use to calculate the distance to the source is called dispersion.  This is the general term used when waves of different frequencies propagate at different speeds in a medium.  Unfortunately, the dispersion of air, particularly at the low frequencies associated with thunder, is very low.  The sound speed in air is a relatively constant $343\tfrac{m}{s}=0.21\tfrac{mi}{s}$.

*Even if the dispersion were relatively high, you would need to know something about the way the thunder sounded when it started.  This isn't a strong limitation as you would probably be able to pick up on it by listening for closer and farther thunder claps.


What relatively simple method will work?
A trick I learned as a child (perhaps you did too) is to count down the seconds between the lightning flash and the thunder clap.  From this you can calculate roughly how far away the lightning was.  Since the speed of light is so fast as to be considered instantaneous in this situation, the time it took the sound to get to you tells you how far away  the lightning struck.  If the time for the sound to reach you is $\Delta t$, then the lightning was a distance
$$d=\Delta t*v$$
away, where $v=0.21\tfrac{mi}{s}$ is the speed of sound in air.  As an example, if you count $5\ \text{seconds}$ for the sound to reach you, then the lightning would be roughly $1\ \text{mile}$ away.  You can remember to simply divide by $5$ as a rule of thumb.  This calculation gives the distance to the source of the thunder which may be a couple of miles above the ground.
A: I think yes, you can get some distance information from analyzing the thunder sound.  I am basing this mostly on having personally heard many thunderclaps, both far and near, of reasonably known distance to the lightning.
Anyone that has ever experienced a near (100 m or less) thunderclap can tell you it sounds a lot more "sharp" than a distant one, not to mention louder of course.  Let's ignore volume, because lots of things can interfere with received volume.  It will give you some broad measure of distance, but won't be all that accurate.
I think the key is the strength of the high frequencies relative to the low ones.  Air will attenuate the high frequencies relatively more, so more distant thunder will have less high frquency content.  This also makes intuitive sense in that near thunder sounds sharp and sudden whereas distant thunder is a low rumbling sound.
So, do some spectral analisys on thunder of various known distances, and I expect you can find frequency ranges such that the amplitude ratios of these ranges make a reasonably predictable monotonic function of distance.
I think that looking at just duration will not work.  This is because lightning is actually made up of (or can be approximated as) many short segments of the "zap" end to end.  Each segment produces its own thunder, which is why thunder often appears to "crackle".  When you are really close, the sound from the bottom of the lightning is so overwhelming that you tend to not notice the following crackle of the segments higher up (and therefore further away from you).  Also, you don't get as much sound when you are end-on to a segment.  Loosely think of a dipole radition pattern.
I'd be interested to hear what you find if you persue this.  Please keep us posted.
A: If you just want a "rough" idea of how far away the lightning struck, then the answer is yes.  You can use the loudness of the thunder as an indicator of the relative distance (a loud strike will be closer than a faint strike).  More accuracy could be be gained with a loudness measuring device calibrated with known average strength of strikes and how far they struck.
A: There is no way unless you see the Lightning. You need a frame of reference. 
Even radar detectors have a frame of reference.
You need a visual approach. Or einstein to work out some new formula
In anycase, Without seeing the lightning how do you know the sound came from one.
It could be a Scud missile up above breaking the sound barrier.
When lightning strikes close by it does indeed sound with a loud crack like a gunshot rather than the customary rumbling sound we hear when it is further away.
