I think canned lychees are a pretty common sight these days, even in non-exclusively asian markets. Just today at Harris Teeter (local grocery store), I walked past some fresh lychee, cut individually and priced at 3.99/lb. Those people eating something being sold as "lychee nuts," canned lychees or lychee flavored sweets are absolutely missing out on the real thing though. (read: don't buy the Harris Teeter lychees)
While in Taiwan last summer (I know, I'm very behind on blogging. What can I say? Life is more fun to live than to write about), we bought a large bunch of lychees on the way back to Taipei from Taichung. If you walk around in Chinatown, or any other large gathering of asians, this is how you would buy lychees. Healthy lycheese are plump, firm to the touch, and red. The ones shown below are perfect, if ever you need a perfect representation to go by when purchasing lychees in the future. I included a thumb in there to show how big they actually are. The lychees available to Americans are usually slightly larger than the tip of my thumb.
I apologize for the lack of flash, but here you can see how meaty these lychees were. The pit is but 10% of the volume, where normally it occupies up to 50% of the inside volume.
Itty bitty pit. Shown here next to my thumb.