As all decent statistical and scientific software packages, MATLAB contains functionality for fitting distributions and testing goodness-of-fit (GoF). As far as I understand, without knowing data distribution's probability density function, the empirical procedure for GoF testing is two-fold.
The first step would be to fit data to distribution, for which you can use either MATLAB internal functions, or external ones (yours or contributed by the community): http://blogs.mathworks.com/pick/2012/02/10/finding-the-best. The second step is, obviously, to select and perform a proper GoF test, as discussed below.
More details and some nice MATLAB code examples can be found in this relevant discussion here on CV. I think that, in addition to the mentioned in the discussion Kolmogorov-Smirnov, Anderson-Darling, Shapiro-Wilk, Shapiro-Francia and Liliefors GoF tests, it is feasible/important to consider a chi-square GoF test. Along with many others, chi-square GoF test is included in MATLAB Statistics Toolbox: http://www.mathworks.com/help/stats/distribution-tests.html. However, if you don't have access to Statistics Toolbox, you can use either example code from the above-mentioned CV discussion, or the
chi2test() function's code from this course notes document (see pages 7-13).
In regard to the statistical power of various GoF tests, I ran across an interesting research paper, comparing the statistical power of most of the above-mentioned GoF tests (with an unfortunate exception of chi-square GoF test), showed that Shapiro-Wilk is the most powerful test, followed by Anderson-Darling, Lilliefors and Kolmogorov-Smirnov, correspondingly.