Multiple alignments

You could use alignat which is also from the amsmath package.

\documentclass{article}

\usepackage{amsmath}

\begin{document}

\begin{alignat*}{2}
  f(x)&=eqn1                    &&   \\  
      &=eqn2_part1              && +eqn2_part2 \\   
      &                         && +eqn2_part3\\  
      &=eqn3                    &&   \\   
      &=eqn4                    &&   \\  
\end{alignat*}

\end{document}

You'll notice that the alignat environment takes an argument- which is (quoting from the documentation)

the number of “equation columns”: count the maximum number of &s in any row, add 1 and divide by 2.

Using boxes via \phantom is also an option, if alignment characters like && get in the way for long equations:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}
\begin{align*}  
  f(x)&=\text{eqn}_1\\  
      &=\text{eqn}_2\text{-part}_1+\text{eqn}_2\text{-part}_2\\   
      &\phantom{{}=\text{eqn}_2\text{-part}_1}{}+\text{eqn}_2\text{-part}_3\\  
      &=\text{eqn}_3\\   
      &=\text{eqn}_4\\  
\end{align*}
\end{document}

A correction for the spacing around binary operators ({}+) and relations ({}=) is required though. See Herbert's mathmode document for more on AMS environments and alignment.