How can I select every other edge loop. In this example its not too bad to do it manually but it other cases it might be. How can I easily select alternating face loops?
Switch to edge select mode (CtrlTab> Edge)
Select an edge loop (AltRMB) going in the direction you want the edge ring selection to go.
Checker deselect (3D view > Header > checker deselect) the edge ring (you can use the F6 menu to set the number of edges to skip before deselecting one)
Select another edge loop (AltShiftRMB) in the direction you want the edge loops the go.
Press Edge ring in 3D view > Header > Edge Ring.
Note that when using checker deselect numbers > 2, you might get extra edge loops. Switch to face select mode afterwards to get rid of them.
The original text of the question asked about edge loops, yet the image was of face loops. Here's a technique to select every other edge loop.
Note if you are using a version of blender newer than this commit (2.71), then you can skip to step 4.
In vertex select mode (CtrlTab), select two edge loops one edge loop apart (AltShiftRMB), that are perpendicular to the direction you want. Then select a single vertex in between them (ShiftRMB). (This is required because Checker deselect only affects selected geometry connected to the active element. i.e you need one connected selection).
Use checker deselect (3D view > Header > checker deselect), then press F6 to edit the N in nth if you want. If you see that the wrong set of edges (the ones you want to remain deselected) are being kept by the selection, change the Offset value.
Still in Vertex Mode, select the edge loop (AltShiftRMB) in between the original two edge loops.
Switch to edge select mode (CtrlTab). You should see parts of the loops you want selected, plus one crossing loop you don't want. If the wrong parts are selected, back up to step 2.
(Versions prior to 2.71: skip this step.)
(2.71+): Select an edge ring with CtrlAltRMB, then run checker deselect. (Thanks to ideasman42 for making checker deselect work with edges).
(2.79): Select the edge ring (perpendicular to the loops you want), but leave it selected.
Press Edge Loop in 3D view > Header > Select.
(2.79): Also deselect the unwanted perpendicular edge ring.
I don't think there's a direct tool to do this.
I've been playing with all sorts of methods to try and get the effect you want and only one thing has worked, and it doesn't seem like it should.
If you can end up selecting all the vertical edge loops, with all the horizontal edge loops deselected (I used edge ring select for this (ctrl+alt+r-click), but it does mean you're making as many selections as you have horizontal divisions, so a quicker way to do that would help), then you perform a "Select Loop Inner-Region", it should, if it behaves the same as my 2.68 install, actually leave you with alternate face loops selected as in your screenshot.
Bit of a hack perhaps, but there it is.
Change to polygon mode
Press Alt + Right mouse button to select loop (or left if you have changed defaults). Where you click on the polygon determines which loop is selected. You want to click in the upper half of a polygon near the top edge in the middle
For subsequent loops also hold down the Sift key while you Alt + click to add to the current selection