Wingreen & Botstein who run the graduate systems biology course at Princeton wrote a paper about how to teach the subject (Wingreen & Botstein, 2006). In the paper they highlight the key concepts they think are crucial to understanding modern systems biology, and they teach the course through discussion of seminal papers in the field.
Here's the reference...
Wingreen, N. & Botstein, D. (2006) Back to the future: education for systems-level biologists. Nature Reviews Molecular Cell Biology. 7 (11), 829–832.
The paper is unfortunately not open access, so for those who can't access the paper edit: @uvesten found a free PDF copy! I have listed their choices below, along with the key concept they think each provides...
Robustness (i.e. retaining function despite fluctuations)
Barkai, N. & Leibler, S. (1997) Robustness in simple biochemical networks. Nature. 387913–917.
Eisen, J.A. (1998) A phylogenomic study of the MutS family of proteins. Nucleic Acids Res. 264291–4300.
Microarray analysis (and more generally, the importance of data visualisation)
Eisen, M.B., Spellman, P.T., Brown, P.O. & Botstein, D. (1998) Cluster analysis and display of genome-wide expression patterns. Proc. Natl Acad. Sci. USA. 9514863–14868.
Individuality of elements in a system:
Elowitz, M.B., Levine, A.J., Siggia, E.D. & Swain, P.S. (2002) Stochastic gene expression in a single cell. Science. 2971183–1186.
Felsenstein, J. (1981) Evolutionary trees from DNA sequences: a maximum likelihood approach. J. Mol. Evol. 17368–376.
Goldbeter, A. & Koshland, D.E. (1981) An amplified sensitivity arising from covalent modification in biological systems. Proc. Natl Acad. Sci. USA. 786840–6844.
Hodgkin, A.L. (1958) Croonian Lecture, ionic movements and electrical activity in giant nerve fibres. Proc. R. Soc. Lond. B. Biol. Sci. 1481–37.
Hopfield, J.J. (1974) Kinetic proofreading: a new mechanism for reducing errors in biosynthetic processes requiring high specificity. Proc. Natl Acad. Sci. USA. 714135–4139.
Random processes and distributions:
Luria, S.E. & Delbruck, M. (1943) Mutations of bacteria from virus sensitivity to virus resistance. Genetics. 28491–511.
Stable switching between states:
Novick, A. & Wiener, M. (1957) Enzyme Induction as an all-or-none phenomenon. Proc. Natl Acad. Sci. USA. 43553–566.
Smith, T.F. & Waterman, M.S. (1981) Identification of common molecular subsequences. J. Mol. Biol. 147195–197.
A good place to start in this subject is the Synthetic Biology network: