Mk14 (http://mymk14.co.uk/paulRobson/emulator.htm) - this is a difficult emulator to run but only because it correctly copies the MK14. If you can spend enough time finding information and a decent manual then it will work properly.
EightOne (http://www.chuntey.com/) can emulate all Sinclair computers from the ZX80 to the QL. The QL emulator crashes on my machine.
XTender and XTender2 (http://www.delhez.demon.nl/) are emulators for the ZX81. They can run ZX80 code (since the ZX81 is backward compatible) but they do not accurately duplicate the ZX80 experience. Both are Shareware, you can run for a defined period (21 days) to test it and it then costs (at the time of writing) 20 US$.
By far the best is Spectaculator (http://www.spectaculator.com ). This is a shareware product which runs for 30 days and you must then purchase a code to continue. This is £16.50 at the time of writing. I have yet to find anything that will not run on Spectaculator including Sinclair ROM images. It also makes a better job of mapping the keyboard.
A good free version is zx32 (search Google for a current download site). It usually works though is not quite a robust as Spectaculator though to try things out, it is a good product.
There are a new of very good QL emulators:
QLAYW (http://web.inter.nl.net/hcc/A.Jaw.Venema/ )- A very good freeware emulator though you must remember to turn down the keyboard repeat as it is very fast on modern computers.
QPC (http://www.kilgus.net/ ) - This one is shareware. It comes with a demo version which works fully except you cannot save anything. The full version costs E59.90. The writer has tried to make a QL as though it were designed today with Windows-like GUI. It is a very professional product but is more aimed at people who want to work on the QL rather than a true emulator.
QLAY2 - this is an update of QLAYW. It emulates the later QLs when people had replaced the Sinclair ROM with something better and added the Toolkit II ROM. In my mind, this is the one to use.
I am only aware of one which is Z88 Dream. It is not especially easy to use but only because it properly emulates the rather limited Z88 screen. This is one case where it is much easier to use the original which are not too difficult or expensive to find.