I have heard people giving reasons left and right why they should have things equiped at 1080i or 720p. I want to give a simple breakdown whats good for what. The main assumption when viewing either format is that your screen has a ratio of 16:9 which is optimal for either resoltuion. This is less of techinical breakdown and more for practical usage.

720P:
It has 720 lines progressivly scanned to the frame, so you see a total of 720 lines from the picture in front of you. Most sports broadcasts which are in HD are set at 720P because it shows fast moving motion very clearly. So for sports events, games, and high paced action games your better off at setting your machine to output at 720P.

1080i:
It is 1080 lines interlaced to produce a very beautiful image. The slight issue with 1080i is that HDTV sets must de-interlace the input to put it to screen. It all depends how well your screen can handle that process to produce the right image. For slow movies, and images 1080i is superior to 720P, but it may not be the best choice for movies with too much motion.

Now that 1080P is slowly becoming standard on the new LCD and Plasma screens all you have to make sure is that your DVD player and other electronic products output at that level. Even for DVDs which aren’t outputing at 1080P the screen resolution will look better overall.

Link: 720P Wikipedia
Link: 1080i Wikipedia