Here is a picture of The Narrows Condominiums, which was St. John's tallest under construction. The condo may be completed seeing these were taken in July by Architype.
I'm not sure what is the current tallest in the city is, there is a new residence being built at Memorial University but the size of it isn't exactly known it was suppose to be 6 stories at one point.
The YMCA is also building a new multi-purpose centre, again the height is unknown. Here is a link to see pictures of it.
http://www.ynortheastavalon.com/building_concepts.php
As well construction is getting ready to start on a new building for the military. It will be a 4 storey building with a total building height of approximately 21 meters.