It certainly depends on the game, but in general, yes. Especially with games that have a progression system (such as RPGs or games like Metroid), I like firing-up a new game just to get that feeling of starting fresh. Most people hate it because they're so used to the power that they had before, but for me it gives a feeling of "Wow, so this is where I started" after knowing how powerful you can get later in the game.
I also love the feeling of openness now that I'm on a fresh playthrough; maybe I'll go for a different character build, or maybe I'll anticipate how I'll handle certain encounters that didn't go so well the first time. Anytime I start a new game of FFVI, for example, there aren't really builds, but I always look forward to some pivotal moments like when the story splits into three segments, or when you first get Materia, and others.