In no particular order:
1. You have complete control of when you watch them
2. You can watch episodes back to back (especially helpful with serialized stuff)
3. No distracting logo (and by extension, no distracting animated logo designed to keep diverting your attention from the show)
4. No commercials
5. Can skip or at least fast forward through the “previously on” bits
6. Can skip or at least fast forward through the theme if you so choose
7. Usually better picture quality
8. If you’re a Canadian, no risk of the start and endings of episodes being cut off by Canadian station’s tendency to cut into American stations that share the same show at the same time slot
9. No risk of sports delaying/cutting off the start of an episode
10. No risk of special reports cutting into an episode
11. No risk of reception issues causing you to miss an episode or have it be blurry
12. If a show’s been cancelled you can often see the episodes that were finished but never aired
13. If episodes of a show were aired out of order, most DVDs place them in the right order (in the case of shows like American Gothic which are packaged in the wrong order you can at least do research and watch the episodes in the order you choose.
14. You can watch shows that are not available in your area or in your cable package
15. Where there’s more than one version out there, you can usually opt to watch the uncensored version of the show.