System identification packages
The System Identification Toolbox contains facilities for 


Linear system identification and determination of transfer function
Non-linear "black-box" models
ODE parameter estimation
Time series identification


One of the more promising substitutes for all of this functionality would be to use R.  Two packages that incorporate some of the time series functionality are the Time Series Utilities and Analysis package and the Flexible Modeling Environment for  Inverse Modelling, Sensitivity, Identifiability, Monte Carlo Analysis.  Also sharing these functions was the Time Series Analysis and Control package

An option for the transfer function calculation and manipulation (which attempts to be a substitute for the Matlab Control Systems toolbox, which overlaps with the System ID one significantly) is the Control Systems Library for Python, but the CSL doesn't have any functions for dealing with system identification, just the ability to manipulate transfer functions (thanks to JasonS for pointing this out).  The Ch Control System Toolkit allows one to model linear systems and determine the transfer function.

I'm sure there are other examples, but they may take some digging to uncover.