Weights of identical twins since they are essentially the same, this is dependent
The effectiveness of two different brands of ibuprofen Different groups, so independent
Effect of a new training program on time taken to complete a task, measured by a "before" and "after" test if the same people are used in both before and after and their data is matched, then this is dependent.
Test scores of a group of students on a math test and a biology test. Dependent. There is likely a pretty good correlation between the same students math score and biology score, but it is not dependent in the same way as a matched set of data.
