iOS: Is there a limit in the number of applications I can leave "running background" in the bar?
Fraser Spiers recently did an excellent article and follow-up video on this question on his blog.

In short, to paraphrase: you don't "leave apps open". By pressing the Home button, you signal them to enter the Background state, from where, depending on how they're written, they are either immediately moved to the Suspended (not-running) state, or are Suspended after completing a certain amount of background processing (such as completing a download).

As Fraser explains, there is no need to manage the number of apps in the 'multitasking tray' except in the case where a specific app stops working and needs to be forcibly restarted.

Indeed, that tray is merely a "recently running" list; there's no way to know at a glance which of those apps have been Suspended and which have not.