What is the range of Unicode Printable Characters?
What you should do is pick a font, and then generate a list of which Unicode characters have glyphs defined for your font. You can use a font library like freetype to test glyphs (test for FT_Get_Char_Index(...) != 0).
First, you should remove the word 'UTF8' in your question, it's not pertinent (UTF8 is just one of the encodings of Unicode, it's something orthogonal to your question).
Second: the meaning of "printable/non printable" is less clear in Unicode. Perhaps you mean a "graphical character" ; and one can even dispute if a space is printable/graphical. The non-graphical characters would consist, basically, of control characters: the range 0x00-0x0f plus some others that are scattered.
Anyway, the vast majority of Unicode characters (more than 200.000) are "graphical". But this certainly does not imply that they are printable in your environment.
It seems to me a bad idea, if you intend to generate a "random printable" unicode string, to try to include all "printable" characters.
See, http://en.wikipedia.org/wiki/Unicode_control_characters
You might want to look especially at C0 and C1 control character http://en.wikipedia.org/wiki/C0_and_C1_control_codes
The wiki says, the C0 control character is in the range U+0000—U+001F and U+007F (which is the same range as ASCII) and C1 control character is in the range U+0080—U+009F
other than C-control character, Unicode also has hundreds of formatting control characters, e.g. zero-width non-joiner, which makes character spacing closer, or bidirectional text control. This formatting control characters are rather scattered.
More importantly, what are you doing that requires you to know Unicode's non-printable characters? More likely than not, whatever you're trying to do is the wrong approach to solve your problem.
This is an old question, but it is still valid and I think there is more to usefully, but briefly, say on the subject than is covered by existing answers.
Unicode
Unicode defines properties for characters.
One of these properties is "General Category" which has Major classes and subclasses. The Major classes are Letter, Mark, Punctuation, Symbol, Separator, and Other.
By knowing the properties of your characters, you can decide whether you consider them printable in your particular context.
You must always remember that terms like "character" and "printable" are often difficult and have interesting edge-cases.
Programming Language support
Some programming languages assist with this problem.
For example, the Go language has a "unicode" package which provides many useful Unicode-related functions including these two:
func IsGraphic(r rune) bool
IsGraphic reports whether the rune is defined as a Graphic by Unicode. Such
characters include letters, marks, numbers, punctuation, symbols, and spaces,
from categories L, M, N, P, S, Zs.
func IsPrint(r rune) bool
IsPrint reports whether the rune is defined as printable by Go. Such
characters include letters, marks, numbers, punctuation, symbols, and
the ASCII space character, from categories L, M, N, P, S and the ASCII
space character. This categorization is the same as IsGraphic except
that the only spacing character is ASCII space, U+0020.
Notice that it says "defined as printable by Go" not by "defined as printable by Unicode". It is almost as if there are some depths the wizards at Unicode dare not plumb.
Printable
The more you learn about Unicode, the more you realise how unexpectedly diverse and unfathomably weird human writing systems are.
In particular whether a particular "character" is printable is not always obvious.
Is a zero-width space printable? When is a hyphenation point printable? Are there characters whose printability depends on their position in a word or on what characters are adjacent to them? Is a combining-character always printable?
Footnotes
ASCII printable character range is \u0020 - \u007f
No it isn't. \u007f is DEL which is not normally considered a printable character. It is, for example, associated with the keyboard key labelled "DEL" whose earliest purpose was to command the deletion of a character from some medium (display, file etc).
In fact many 8-bit character sets have many non-consecutive ranges which are non-printable. See for example C0 and C1 controls.