How can I prevent games from dragging on? How can I prevent a game from dragging on, taking 60+ moves to get anywhere near finishing?

I mainly encounter this when playing people at or below my level (~1400). This never happens when playing someone better.

I recall reading somewhere that most games should ideally be finished in about 30 moves or so. That seems reasonable.

What can I do to prevent a game from dragging on without giving myself a disadvantage?
Seriously, by checkmating your opponent.  If every game is going on for 60 moves, the bad news is that you don't know how to score the win.  The good news is neither does your opponent.

But by merely recognizing something is amiss, you have gained a huge advantage.

Now, you have to sharpen your game.  The next step is for you to figure out why you can't win sooner.  The moves are there - you know that a GM could win either side of the board pretty much up to the bitter end.  The moves are there.

I don't know if it is appropriate for this site, but post a game (you DO keep notation of your games, don't you??) and we'll look at it.  Post a typical game, regardless if you won it or not.  And don't worry about the quality of the game.  There's always a bigger fish.

Edit - I'm like a broken record on this, but another way is to run your games through a chess engine.  Every move, both sides.  Set the engine's strength such that it can beat you every game.  See the moves it suggests instead, and when it finds a move markedly better than the one you chose, find out why it made that choice.  Figuring this out is a lot of work, but getting better at chess is not often easy.