There are a couple of very odd pangrams (no repeated letters) referenced at this site and the author states:
Unfortunately, to my knowledge, there are no particularly clever 26
letter pangrams in English. Constructing a sentence that uses every
letter of the alphabet once and no more -- essentially an anagram of
the alphabet -- seems to require the use of acronyms, initials, and
strange punctuation. The most interesting I've seen is, "Glum
Schwartzkopf vex'd by NJ IQ."
There's also this answer in Yahoo Answers:
Best Answer: A sentence that contains every letter of the alphabet
at least once is called a pangram. People have constructed
26-letter-long pangrams using only words that can be found in an
unabridged dictionary, but they don't make a whole lot of sense. The
most famous example is "Cwm fjord bank glyphs vext quiz."