Strange Blue dots???

I'm getting a lot of questions lately on "What are these strange blue dots that have started appearing all over my drawing ever since I upgraded to 2011?".

These are the new Geometric Constraints features. Constraints aren't new they were introduced in 2010 but weren't widely used (from what I've noticed). What these constraints will do is remember the way you have drawn or edited entities in your file. To put it simple, if you select the grip of an object and then use an "object snap" to snap it to a point on another object, geometric constraints will remember that you snapped it there and will from then on always remain connected at the point you snapped too.
If you don't want to use Geometric constraints and aren't sure how they ended up on your file it's probably because you inadvertently click the constraints button on your Drawing Settings Bar at the bottom of your screen.

By Right-clicking on the Constraints button you can also select "Settings", from there where you can better control your constraint settings (the same as you would Object Snaps). If you created Geometric Constraints within your draw and want to remove them just hover over the "Strange Blue Dot" until you see the Constraint tool button appear, Right-click on the button and select "Delete".

Then make sure you have the "Infer Geometric Constraints" turned off so that you don't keep getting them in your file.