Most of the time, I want games to challenge me. That can involve many different things. A lot of my favourites have heavy action and/or themes, and can have be tensed up and on the edge of my seat. I also enjoy more mentally challenging games, including puzzle-solving, or mastering complicated game mechanics or item management.
I find these things enjoyable, but I wouldn't call them relaxing. I wonder sometimes if a game can be truly relaxing. I have a very broad definition of what I will call a game, but I think some interactivity is required. And as soon as there is interactivity there will be consequences for actions, even if that's on an extremely basic level.
If I want a really soothing experience I'm probably not usually going to look to gaming. But, games can still calm me somewhat. I'm sure this is a very individual thing -- one person's relaxing is another person's slow and boring, after all.