A very elaborated answer which demonstrates how to use Mathematica's built-in SQL database to store the cache completely externally:

http://stackoverflow.com/a/5291299/590388

You can also be interested in Leonid Shifrin's Cache.m package. Citing the home page (emphasis is mine):

This package allows one to create a "copy" of a given function of a single argument (Downvalue-based or a pure function), with an internal cache of the fixed size . This cache will automatically store results of the most recent function calls, and use the stored values rather than recompute the r.h.s. in case if the function is called again on the same argument. This may speed-up computations considerably in cases when a function is both computationally intensive and is frequently called on the same values of the argument.

Hm. I think i've found a decision.

f[x_] := f[x] = x^3;
DumpSave["dump.mx", f];
f[0];
f[1];
f[2];
f[3];
?f
Print["======="]
Clear[f]
?f
Print["======="]
<< dump.mx
?f

Out:

Global`f

f[0]=0

f[1]=1

f[2]=8

f[3]=27

f[x_]:=f[x]=x^3


=======

Global`f

=======

Global`f

f[x_]:=f[x]=x^3