A professional
non-linear video editing
application from
Adobe.
Premiere has built-in video capture capability and can capture from either analog or digital sources (via a video capture card or an IEEE 1394 port, respectively). Once captured, the video "clips" can be split into scenes and dragged onto a timeline. The timeline gives a nice visual representation of where each scene fits in the project, with multiple seperate tracks for video, titles, and audio. Titles and effects are easy to create, and can then simply be dragged into place on the timeline.
For the more adventurous, Premiere integrates with Photoshop to allow frame-by-frame manipulation. Want to make a video of a LucasFilm-quality lightsaber duel? It's easy to do if you've got some Photoshop knowledge and a bit of patience. Using Premiere's built-in tools, you can even do bluescreen work or combine multiple seperate video clips into one image to make it look as if you're confronting your clone.
Premiere (like other Adobe products) is expensive. Expect to pay at least $500 retail.