Can the Titans swim?
If you take a look at the official closing theme of Season 2 of Attack on Titan you see the following: 


  Titan emerging from the water. 


But the way that they emerge it suggests


  that they actually don't swim but cross bodies of water by walking along the bottom. 


Also from the scene we can derive that


  if titans can walk along the bottom of bodies of water this implies that they either have no lungs or do not require oxygen for survival which is something that was actually discussed on Anime Stack before. 


And finally we can see that


  water does not harm them in any way whatsoever.