When you long-press the Home button, is that bringing up only recently used apps and processes, or ones that are currently using the phone's resources (and thus consuming power)?
and you can swipe them to the left to close them if you so desire.
If you are looking to close apps that may be running in the background, tap the left "menu" icon just below the screen and choose manage apps to close any background apps that may be consuming battery and data.
That is a list of the recently used apps yes, but swiping them left or right will not close them it just removes them from the list there. Just to be clear, if you want to close them do as YellowJacket suggested and by going under APPS and then Running and you can click on it and close it from there.
Another interesting thing I've noticed about the list of recently-used apps - if an app is opened from within another app, the child will not appear in the list. For instance, if you browse your SD card with Astro, then open an image file from there with My Gallery, only Astro will appear in the list. Not My Gallery, since it was called from within Astro.