Bill,
That's one of those "sort of" kind of questions. It depends a lot
on the particular receiver and what frequency range you plan to listen
to, and then on the amount of space you have for an antenna.
In general, receivers that listen to the lower frequency bands, HF
for example, are more sensitive than those that are used for the
higher bands (VHF, UHF, SHF). That means that to hear a typical
signal a specifically designed antenna having the exact output
impedance as the receiver's input impedance isn't required. Almost
anything will work to some extent. The receiver just isn't that
'picky', since it typically has more 'hearing' ability than required.
There's a 'catch' though. Reducing the amount of signal losses in
that 'whatever' antenna is going to make the resulting signal getting
to the receiver that much stronger. Something always nice to have,
but there are practical limits. If that 'whatever' antenna meets your
requirements, then it's as 'good' as anything, sort of. If it
doesn't, then making that antenna less 'lossy' is also nice. That
"less 'lossy'" thingy also includes making it directional, longer,
shorter, higher, whatever, to increase the amount of signal getting to
the receiver. So, looking at it from that point of view, the antenna
ought'a be reasonably 'close' to what will typically 'work' well on
the received frequency. Huge range in that 'close' quality and the
definition of what 'works' means.
There is no 'perfect', 'do everything', antenna. Just too many
factors involved. 'Higher' and 'longer' tends to 'work' better than
'lower' and 'shorter', in general. Which, like any generalization, is
never always true.
That's the sort of 'long', half-assed, technical answer. The
'quick-n-dirty' answer is, no, they don't have to be 'matched' to the
receiver. Which says nothing about transmitters.
- 'Doc

[all puns intended]