Okay here's the rundown:

Composite Cables (Yelow, Red, White) [aka RCA Cables]:
Introduced in the 1950s, they carry an analog signal.
Max Resolutions:
720 x 576i @ 50
720 x 480i @ 59.94
Used for Consumer electronics, including VCR and LaserDisc, 1970-1980s home computers like the Commodore VIC-20, 1980s-1990s video game consoles, some laptops.

Component Cables (Red, Green, Blue and sometimes Red, White):
Introduced in the 1990s, they also carry an alalog signal, but break the video into seperate sources for higer resolution and clarity.
Max Resolutions:
1920×1080 @ 60
1280×720 @ 60
720×480 @ 60
Took the place of Composite Cables in most home electronics. (DVD players, Blu-Rays, Video Game systems, etc.) Also, allows 720p and 1080i HDTV connections.

DVI Cable (Digital Visual Interface):
Introduced in 1999, this carries either analog or a digital video signal. No audio however.
Max Resoultion:
2560 x 1600 @ 60
Standard for PC Video Cards and also included on HDTVs before the HDMI protocal became standard.

High-Definition Multimedia Interface (HDMI):
Digital only, but also carries all digital audio codexs. Also includes High-bandwidth Digital Content Protection (HDCP). Encryption is mandatory.
Max Resolutions:
2560 x 1600 @ 75
4096 × 2160 @ 24
Now standard for most high end home electronics. (1080p HDTVs, Blu-Ray, some upscaling DVD players. Next-Gen Videogame systems, PC)

There are others such as Display Port and Serial Digital Interface, but the above are all you need to know regarding most Home Entertainment Devices.

S-Video, or Separate Video (Not "Super" Video as commonally nicknamed), is an inbetween of Composite and Component. It does not carry audio and breaks the analog video signal into two sources: luminance & chrominance. Basically Gray-Scale and Color-Scale.

Max Resolutions are same as Composite Cables:
720 x 576i @ 50,
720 x 480i @ 59.94

S-Video is also the second poorest, quality-wise, being far surpassed by the more complex component video schemes, such as RGB. What distinguishes S-Video from these better component-video schemes is that S-Video carries the color information as one signal. This means that the color has to be encoded in some way, and as such, NTSC, PAL, and SECAM signals are all decidedly different through S-Video. Thus, for full compatibility, the connected devices not only have to be S-Video compatible, but also compatible in terms of color encoding. In addition, S-Video suffers from reduced color resolution. NTSC S-Video color resolution is typically 120 lines horizontal (approximately 160 pixels edge-to-edge), versus 250 lines horizontal for the Rec. 601-encoded signal of a DVD, or 30 lines horizontal for standard VCRs.

The only difference the the case of 720p over cables is that the Component is analog and the HDMI is digital. You may or may not notice a difference.

If you have the choice, always go HDMI. One cable for video and sound and all in one cord. Easier to setup. Cleaner looking and easier to work around.

And, don't believe that HDMI cables are expensive, because they aren't. The retail stores like Best Buy and such charge stupidly high prices for them. Get them through local warehouses or onine vendors. www.nwca.com and www.newegg.com are great choices. And, you will notice absolutely no differnece between the $60 Monster cable at bestbuy over the $12 cable through online.

Quote:

What about Laser 7 output?

You don't have to worry about that unless you're Cartman.

I should add though, make sure to get HDMI 1.3 cables, as they are current spec, and some 1.0/1.1/1.2 cables may not like newer Blu Rays and HDTVs.

720p vs 1080p is Component vs HDMI.

If you look at them side by side, you'll notice a huge difference. However, if you're watching or playing something on 720p, it will still look fantasic.

1080i=interlaced vs 1080p=progressive

1080i, the former king of the HDTV hill, actually boasts an identical 1,920x1,080 resolution but conveys the images in an interlaced format (the i in 1080i). In a tube-based television, otherwise known as a CRT, 1080i sources get "painted" on the screen sequentially: the odd-numbered lines of resolution appear on your screen first, followed by the even-numbered lines--all within 1/30 of a second. Progressive-scan formats such as 480p, 720p, and 1080p convey all of the lines of resolution sequentially in a single pass, which makes for a smoother, cleaner image, especially with sports and other motion-intensive content. As opposed to tubes, microdisplays (DLP, LCoS, and LCD rear-projection) and other fixed-pixel TVs, including plasma and LCD flat-panel, are inherently progressive in nature, so when the incoming source is interlaced, as 1080i is, they convert it to progressive scan for display.