Rectangular Selection
This tool is convenient and quick for any rectangular shaped objects but if the rectangle is skewed at all or if there is a shape that is not a rectangle this tool is basically useless.
Elliptical Selection
This tool is useful for both circular and elliptical shapes, it can be used with perfect circles and circular/oval shapes. This tool wont work for any other shape and the edges are very harsh.
Magic Wand Tool
The magic wand tool selects areas of the same color which is convenient for selecting large areas of solid color, the hue tolerance can be adjusted to include more colors similar to the selected area. This tool isn't great for selecting edges because the colors tend to vary.
Quick Selection Tool
The quick selection tool is good for selecting foreground objects and areas of contrast, you can click and create a selection and keep clicking to add to it or you can just drag over the area you want. The downside is sometimes it will select outside of the area you want because the contrast is lower.
Lasso Tool
This tool is good for uniquely shaped areas but it is freehand which means it's subject to drawing error.
Polygonal Lasso Tool
This tool is useful for selecting areas with straight lines that are not a perfect square or rectangle, it can be difficult to accurately select the corners.
Magnetic Lasso Tool
This tool snaps to the edges of an object and you can drag around the edges of an object to select the whole area. The difficult thing about this tool is that it sometimes incorrectly snaps to edges because there is not enough contrast between the foreground and the background.
Pen Tool
The pen tool is ideal for objects with curves and for selecting oddly shaped areas, you can adjust the curve you create as you go. The tricky part is that sometimes the curve produced is dependent on the previous point you made and you might have to go back and adjust.