Some apps, like my browser, mail program, the terminal, Emacs, ... I love having start quickly, even if it's because they were just in the background before.
Other stuff, like Preview, I don't use often enough to care about the load time, and I would probably configure it to exit when the last window closed.
Under Lion, that is (sort of) what Preview and TextExit do. When you close all open documents in Preview and then switch away from the app, the app will terminate.
Basically with command held down the entire time, hit tab until Preview is framed, and instead of releasing command (which would pull Preview to the foreground), hit Q, which will send Preview the command-q event and cause it to quit.
I do not understand what you are saying. Can you elaborate?
Edit: As to my original comment, when I switch to another app, preview stays open, but up to now I don't know how to close it because I can't get the menu to appear without a pdf or something using it, that's why I reopen a document, forcing the menu to show up, then close the app.
As far as the menu disappearing when you close both documents, that's confusing and directly contradicts what you typed earlier. I can open Preview.app, and it'll just show me the menu. I can close it by alt-tabbing to it and hitting Cmd-Q - no windows required.
That's the whole paradigm. Windows belong to applications, but applications aren't windows. That's one reason the menu bar is divorced from any window (along with Fitt's law): so that you can interact with an app even when it currently has no windows open.
You could just close it from the dock you know. Or switch to it and command-Q immediately.
In fact, I don't even understand how you'd go around to "reopening a window" of preview, preview will not open any window without a document in it, do you open a document just to close preview or something?