Taverna will run tasks in parallel whenever it is possible. In fact you have to put effort into serialising execution if it is needed, by using Run after option to run one service only after another has finished.
Taverna 2.x uses stream of data items, which means that services which just “pipe through” items of a list can start processing (in parallel) when the first item has been outputted upstream. This can be compared to iterators in Java. For detailed information see the lists and iterations.