A man and a woman, both with brown-hair, have three children. The
oldest with blonde-hair, the middle child with red-hair, and the
youngest with brown-hair. Is this possible at all? I realize that if
both parents carried the recessive gene for red-hair, two brown-haired
people could have a red-haired child, but could they have a
blonde-haired child as well? Or would infidelity have to be involved
somewhere?

That's roughly the situation in my family. Except the order of the
children: the oldest has brown hair, the middle is blond & the
youngest is red-haired.
My 2 brothers and I, the F1 generation, do look somewhat similar, and
somewhat like our dad.
Not that this completely rules out infidelity, of course :-)

But I don't know that hair-colour is a single locus trait. More
likely, it's a lot more complex than that. Here's an overview on coat
colour of horses - the mechanisms probably aren't that different from
hair colour in humans:

http://www.vgl.ucdavis.edu/research/equine/lvmillon/coatcolor/coatstxt.html

Also, a brief explanation of how/why some *humans* have red hair:
http://www.science.edu.sg/ssc/detailed.jsp?artid=6291&type=6&root=4&parent=4&cat=40

I looked for [hair colour genetics], and I mistyped Mendelian in [hair
colour mendelain] :-)

Though much more complicated, hair color is determined by the AMOUNT
and TYPE of melanin pigmentations (eumelanin and phomelanin).

That is :

Eumelanin AMOUNT [HIGH] Black<--> Brown <--> Blond [LOW] and
Phomelanin AMOUNT[HIGH] <-- Reader/redish 

The amount and type of melanin is determined or affacted by:
 
1. Genes (MULTIPLE) not only with Dominant-Recessive model but also
with additive or with a discontinous variation.
2. Environment (Sun, chemicals...)
3. Age
4. Gender


For more search : inheritance human hair color genetics

http://www.gnxp.com/MT2/archives/001516.html
http://www.science.edu.sg/ssc/detailed.jsp?artid=6291&type=6&root=4&parent=4&cat=40
http://biology.plosjournals.org/perlserv/?request=get-document&doi=10.1371/journal.pbio.0000027
  (skin)

whoops! it should be continous variation, where series of intermediate
phenotypes  excist (NOT discontinous variation).