Right now, there is a hard-coded limit of 1 megabyte per block.
If we assume that limit never changes, that gives:
1MB per block * 6 blocks per hour * 24*365.25*200 = 10,519,200 MB
... or 10.5 terabytes for the maximum size of the entire blockchain over the next 200 years (somebody check my math, I'm really good at dropping zeroes).
I expect that in 200 years 10 terabytes of storage will cost a few pennies.
Now whether or not that 1 megabyte per block limit should go away is hotly debated, and will be debated more and more as transaction volume increases.