If we knew their final protein structure, it would be much easier to work out what biological processes they may be involved in.
Also, taking known protein structures and learning more about how they may interact with other proteins would be extremely useful. For example, a large number of molecular pathways in cancer are fairly well described in a general sense, but lack specific information on the actual reactions.
Finally, being able to put it all together in the context of mutated genes (which we can now screen for fairly easily) and being able to determine what impact a mutation may have on the protein (can it still be formed, how will it interact in a pathway?). For example, some mutations break a protein completely, while others may impact "switch" genes, leaving them in a permanently "on" state preventing them for reacting to external signals [2].
This kind of thing is really important in cancer research (and one day treatment), where the function of specific proteins may be the difference between life and death.
[1] http://www.genecards.org/cgi-bin/carddisp.pl?gene=C1orf186 [2] http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1891745/