I'm not sure there is a definitive answer yet. This is how I see the options.
The trees have used arrows pointing to the right for the closed and down arrows to open, which, as FreshCode mentions in its response, has been generalized to expanders. It is a reasonably well established convention, dating back to Vista for Windows and in the mid-1990s for Mac (where they were known as "little arrows").
I have worried that it may cause confusion. In other uses of arrows such as cascading menus, split menus, menu buttons and drop-down lists, the arrow suggests only a temporary display of some options, not the fixed opening of a complete panel that must be explicitly closed. Also in these other uses of the arrows, the direction of the arrow inevitably indicates the user's movement. get in activation On the contrary, in trees or expanders, the arrows pointing to the right cause a downward movement and the arrow pointing downward causes an upward movement. I have not witnessed this being a problem (for example, users think that the down arrow means "expanding further"), but I have not witnessed extensive use of the expander.
Window Control Agreements
Perhaps it would be better to use a down arrow to mean closed so that at least the direction of the arrow is consistent with the movement it creates and with its use in other controls. An open expander would have an "close" X icon, taking advantage of its use for Windows. However, users may think that "X" means Delete as in "delete all that entry that I just put in the expander", so users are afraid to close an expander.
Perhaps a more appropriate way to use window controls is to use the minimize and maximize icons for open and closed expanders, respectively. However, any use of window control conventions is probably more effective if the controls are on the right, as they are for Windows. This can induce an additional rotation of the mouse since the input controls tend to be justified to the left. In addition, I would worry that users confuse the expander controls with the window controls when the expander moves to the top of the window.
Other tree conventions
Using "+" to mean closed and "-" to mean open is an alternative seen in tree controls prior to Vista that avoids the contradiction of the directionality of the arrow. It seems to work fine, but, like most of the options I've covered so far, I've always wondered if some users are confused about whether the symbols are supposed to represent action the user is activated or activated state of the expander (assume that "-" means that the expander is closed, or at least not completely open).
Another one that is worth considering are the "touch" icons used by Java Swing.
For some reason, I feel they handle the action / state problem less ambiguously.
The usual way I recommend dealing with the action / status problem is to use toggle buttons as I described when responding. Should an icon show the current or next status? In this application it means that you use the same icon that means "open this" (I think the plus sign is less ambiguous) to both of them closed and open expanders, but the icon button has a high appearance for closed expanders and a depressed appearance for open expanders.
Didn't I mention any definitive answer?
With so many problems, I don't think we really know which one is the best without some user tests. It is completely possible that it does not make such a difference. If you finish the test, post your results here.