What are the benefits of elucidating the crystal structure of a protein?
Protein structures, which can be obtained from protein crystals or from concentrated solutions of pure protein via NMR, are arguably the primary source of knowledge that we have about how genes perform their function on the molecular level.  

I've added a link to RCSB.org above - they write up a story on an important protein structure monthly(?) - its a great way to pick up some fascinating stories. 

The precise atomic positions from a protein structure are indispensible for several reasons.  Since biological processes are all fundamentally chemical ones.  The specific positions of the atoms reveal how proteins, nucleotides, lipids, drugs and other biological molecules specifically interact.  

Examples:


Protein structures broke the ground in biological inheritance (Watson / Crick / Franklin's DNA structure) 
Protein structures of lysozyme and proteases were the first to show exactly how proteins bind their substrates and enzymatically catalyze chemical reactions.  
Protein structure of hemoglobin in both oxy- and deoxy- forms (i.e. with and without oxygen bound). showed that proteins change their spatial arrangement to modulate their function.  


This list goes on to more recent breakthroughs in how signals and molecules interact with the cell through the membrane.  There is literally no topic in cellular biology which has not substantially benefitted from having a protein structure revealed. 

The advantages of working with protein crystals are that they can be larger proteins and certain kinds of difference experiments an be more easily performed when a protein crystal is obtained.  For instance if you have a crystal of a 100 kDa (~900 amino acid) protein, you can often find the binding pocket of the enzyme without a tremendous amount of work. 

The disadvantage of working with protein crystals, as you probably know well is that getting crystals is often a quixotic effort soaking up months or years, often with little or no results.  Pretty demoralizing until you hit the target.  

If you're astounded to think that proteins, which are often hundreds or thousands of times larger than a salt or mineral you usually find in crystals...you are dead on.  The crystals are often very tiny - a decent sized crystal measures about a millimeter on one side, but often are only a fraction of that size.  That's why protein crystals often are taken to synchrotrons, linear accellerators or other free electron X-ray sources which are millions (?) of times more intense than a dental x-ray. I would guess that most protein crystal structures are obtained using special beamlines created especially for biological crystallography. 

That sort of tells you the funding priority science is willing to put into x-ray protein crystal structures.  Simply the idea that protein crystals might be easier to grow in microgravity (along with the low weight of the experiment) justified over a decade of protein crystal growth experiments on the shuttle and ISS.  

Interesting note: The Guardian (which is based in the UK where crystallography, protein or otherwise started out) has posted a short video outlining highlights of crystallography's contributions over the past 100 years.  If you watch assiduously you will see protein crystallography cropping up with a litany of nobel prizes.  

New thoughts: 
There are signs that crystal structures are coming to an end.  Using an electron micrograph to simply take a picture of many thousands of individual proteins laying about can be digitally averaged to create low resolution structures they are gradually becoming higher resolution and are a lot less work than preparing and making a protein crystal - and it works well on larger proteins and protein complexes!