Is there a way to save more replays in your history in StarCraft II?

You can save more than 10 replays if you actually hit the save replay button on the game. There is no limit on the number of saved replays you have. The 10 is how much of a history it automatically saves for you. The 10 history limit was included near the end of the beta. I have not heard of any way to increase this limit, but there are some alternatives.

If you want to automatically save all your replays, a couple solutions are available here. Note: the methods there are not exactly short or quick to set up, but do get the job done.

As an alternative, you can install sc2gears and it has a feature to auto-save games It requires that you leave it running while playing though to do this.

Edit/Interesting note: I can't confirm this at the moment, but if you navigate to your unsaved replays folder, I believe you will find that it actually keeps 25 rather than 10 replays in there.