Spot Focus reduces the size of the AF point, making it more precise, more accurate, but at the cost of some speed when tracking in AI Servo. It's primarily for situations where you are shooting through blades of grass or tree branches... also useful for really exacting focus for shallow depth of field portraits, macro. Some folks have success with it shooting moving subjects in AI Servo, but I suspect most of the time you'd get a slightly higher keeper rate reverting back to Single Point focus mode. Spot Focus works very well with One Shot. The reason it's slower at tracking... or might miss entirely... is exactly what Frank mentions... less of the scene is being evaluated, so with Spot Focus there's greater risk that there won't be contrast or detail to lock onto.
In Spot Focus mode, the AF point size is reduced in size so that it's within the normal AF point "box" seen in the viewfinder. It's pretty close to the size of the secondary box only displayed in the Spot mode.
As Jeremy noted, the Single Point AF point is actually a little larger than the box indicated in the viewfinder. In partucular it seems to go beyond the top of the box, primarily (when using the camera in horizontal or landscape orientation). The sides and bottom seem fairly accurate.
If subjects are a bit erratic in their movements, try Expansion Points. With this, you select a single starting point manually, and the points around it will kick in if you don't keep the selected point rignt on the subject. Just be aware that if you select a point at any of the edges of the AF point array, it will be limited to expanding only to the points on the three remaining sides.
Zone Focus looks like Expansion, but it's not. It activates a group of points equally. Any one of them can be the starting point and/or take over from it's neighbor if needed. In a sense, Zone Focus is sort of a scaled down version of All Points/Auto Selection. These modes work best when there's little or nothing behind or in front of the subject, that might distract the AF system. Think of a flock of birds flying past you, against a fairly plain sky (some distant clouds usually aren't a problem).
AI Servo Tracking Sensitivity (C.Fn III - 1) can be set on 7D and some of the other cameras. You might try slowing this down initially (-1 or -2). It's actually controlling how quickly the AF will jump to another target, should something come between you and your subject... or how quickly AF will jump to a background if you fail to keep the active AF point on the subject. It doesn't actually change AI Servo speed of acquisition or ability to track at all. Later, as you are more skilled at tracking subjects, you probably would be able to turn this setting back up. I think a faster setting helps a bit if subjects change directions a lot.
On 7D (and probably some others), you also might want to set AI Servo 1st/2nd Image Priority different than the default. This allows you to change how the camera prioritizes AF accuracy vs shutter release for the first shot, and AF accuracy vs tracking accuracy on the 2nd and all subsequent shots in a series. I leave it set on the default 0: AF Priority/Tracking Priority. This tells the camera to emphasize focus accuracy all the time when in AI Servo, even if it delays shutter release slightly or slows down the frame rate during a series of shots (the item before the / is applied to the first image, the selection after the / is applied to the 2nd and subsequent series shots). I just figure I'd rather have in focus photos as much as possible, rather than lots of shots at the highest possible frame rate. Out of focus shots do me little or no good.
I use Single Point about 75-80% of the time. I probably use Spot Focus second most often, maybe 10-12% of the time. I'll use Expansion mode 5 to 7% of the time. The remainder, probably under 5% of the time... i.e., rarely... I use Zone Focus mode. I virtually never use All Points/Auto Selection.
60D is just like the 50D and 40D before it... Best to select a Single Point manually and work to keep it on your target. Because they are all dual-axis, all nine work pretty well. However, the center point is still a bit better and often is the best choice. Set the camera to AI Servo (not AI Focus)... Try using Back Button Focusing.
(BBF works very well on 7D, too.)