If you are worried about the pipe bursting, then, as Pkruse said, you are concerned with the difference in pressure between the inside and outside of the pipe in question.
As Jack_Action said, putting too much pressure on something will cause it to deform and probably fail. However, I doubt you'll find many applications where you will cause the structure of a pipe to fail due to high combined internal/external pressures, with low or null differential, over failing at fittings and the like.
As for your other concern, the fluid will not pull appreciably on the pipe for you to worry about tensile strength. However, you should certainly take care to stabilize the run of pipe. Fluids are dynamic, and you don't want to let a 1000 ft run of pipe go unsupported. You will, however, have to take the weight of the water into account for sizing supports, assuming there is an elbow or something which the weight of water will push against at the bottom of the 1000 foot run.
edit: if your pipe is open at the end, then the water weight will have virtually no effect on the tensile stress of the pipe. I wouldn't worry about that beyond sizing vertical supports.