The ListView.Click event works in the desktop .NET Framework. It doesn't work in the Compact Framework, even in the beta SP3: it doesn't fire.
Nor does it fire in .NET Compact Framework 2.0 Beta 1, which I've been looking at this evening, a bit. You get a warning when you compile:
warning VSD101: Members not supported by the Device platform should not be called: System.Windows.Forms.ListView.add_Click is not a supported method in this platform
It turns out that you're not supposed to use Click - you're supposed to use the overarching ItemActivate event, which is fired when either you click, or double-click depending on configuration, or when you activate the item with the keyboard. I suppose this makes sense for Smartphone, since you can't 'click', the screen not being touch-sensitive.
You configure whether ItemActivate fires on single- or double-click by setting the Activation property on the control.
Note the nice bit of abstraction leakage in the warning message: the line of code reads:
listView1.Click += new EventHandler(listView1_Click);
Er, where did I call the method add_Click? Answer, it's lurking behind that nice += syntax.
OK, so I'm using the wrong semantics; it should still work.