Cognitive Functions Free Tests
The tests are not officially 'online' but they still can be found in the site's archives and they're functional (they will compute your results).
Here you go:
Cognitive Development Survey (attention: Submit link is broken)
This is an extraordinarily accurate test and I very much enjoyed the way it was conceived and carried out. The options are clear and insightful, although I have to stress some of them favor the Intuits as they can get quite abstract.
Interstrength Cognitive Assessment (valid link)
This is the older version of the above test, with a different form of presentation, but equally reliable.
InterStrength Dynamics Assessment (attention: Submit link is broken)
This test is said to be one of the best and one of the most innovative ways to determine your type. It measures the way the opposite cognitive functions work together in pairs (Ti with Fe, Fe with Ti, Si with Ne, Ne with Si, etc), thus studying the functional dynamics and interconnections within the personality, to determine your probable type. Unfortunately I did not obtain a sufficiently accurate result with this instrument, but I nonetheless warmly recommend it to everyone who wants to study the relationships between the cognitive processes more in-depth.