I put a character generator on my website though I display the codes in decimal not hex.
The displayable characters go way up but there are some curious gaps. I can't remember but I probably chose the fonts "Arial, Helvetica, sans serif" (Win/IE, Apple, other) which covers most peoples' installation. Though I haven't tested on Tabs and Smart Phones.

In Firefox 28.0 it displays rubbish between #4625 and #7400 (eg) and it looks to be going Chinese in the region of #12288. Chrome looks to be the same, with nothing above #13311 for a long ways.

Have a play (click here - (new tab/window)) and click on the +100 a few times.

and there is a converter if you are website building and want to hide things like e-mail addresses from web-bots. Not that a clever web-bot would be fooled much these days. But if you surround it with spoof e-mail addresses like william.gates@msn.com and bill.gates@hotmail.com etc etc you are improving the odds - using the halo effect. They play the percentages - so should you.