I use all sorts of on-line systems to help students understand what we're doing on a course. However, I don't rely on 'pure' on-line tests in the sense you're probably meaning (i.e. with both questions and answers on-line, and with some kind of automatic reporting of marks).
Unless the exercise is designed for student self-help, there's always a trained teacher involved in making the assessments. My main problem with on-line tests in the form that they usually exist nowadays is that the information you get from them is either banal or wrong
and they encourage students to be answer-oriented, when I think that learning is process-oriented. Educational administrators usually love them because they generate numerical information
but that kind of information is usually pedagogical nonsense.
To give you one example, in Sweden, when you learn English, you'll come across a 'some and any' question in most on-line grammar tests. To test them, I always look for the question that says something like:
Would you like *** tea?
and the one which says:
I don't like *** of them.
(*** = either 'some' or 'any').
The pre-programmed answer is 'any for both of these
but any native speaker can tell you that either is equally acceptable - provided you specify the context. In fact, 'would you like some tea?' is actually much more likely to heard by a Swedish learner of English.
I often hear an argument which says "well, OK, they're flawed, but aren't they something to use whilst we wait for something better to be produced?". I'd say, no. It's better to put your efforts into more meaningful activities
but these almost always involve trained and experienced teachers, people who are rarely involved in the production of on-line tests.
You're welcome to take a look at my Toolbox page, where I've collected together some of the on-line 'tests' I use with my students:
http://www.humsam.hik.se/distans/existstud/toolbox.htm