I keep hearing of people loading their sgs with a combination of slugs and buckshot for home defense. What are the advantages of this, and what's the best lineup for an 870 with an eight shell capacity?

Years ago this was known as "Dutch Loading", for some reason.

In a true home defense gun, this doesn't have much real utility, since the distance inside a home is so limited, there's no need for a different mix of shells, most anything will work.  
In typical "real world" defense situations, the only reason for choosing a lighter or heavier buckshot, is the distance to the nearest neighbor, and how thin his walls are.  
In the real world, there will be very little need, or justification, to shoot at somebody at any real distance.

However, a classic case for Dutch loading might be for use in a road-block situation for police.
This situation might be a need to stop a car, then engage the occupants.

A Dutch load might be: the first 2-3 rounds out of the mag would be slugs, to penetrate the car body and tires, bring the car to a stop, and reach inside to hit the occupants.

The new few rounds would be #4 or #1 buckshot to engage the occupants at close range as they bail out of the car.

The last rounds out would be #00 buck to reach out to the occupants as they run away and are at longer ranges.

You could reverse the load for a "Bonnie and Clyde" situation:  The bad guys are coming out of a house, jumping into a car, and driving off.

As they exit the house, you'd want #00 to hit them at long range.  As they get to the car, #1 or #4 buck for the closer range, and the slugs for when they've gotten the car moving and are attempting to drive off.

The problem with Dutch loading for a HD gun, is there is little chance of having to shoot slugs at long distance against a bad guy. Usually, if they're that great a distance, they're running away, and you're not legally Ok in shooting at them.

If you can come up with a realistic situation where different mixes of slugs, smaller buckshot, and #00 buckshot would be needed, have at it, but the key words are "realistic situation".  Just remember, shooting at people at longer distances is very rarely necessary, and is often out and out illegal.

faris,

You have a very valid point. I have one simple exception.

The longest possible shot in my house is 21 feet. My last round in the magazine is a Federal tactical slug. It is not for distance, but for precision.

The guys that shoot with me in MN can attest to my "No hostage" drills.

I certainly can attest to your No-Hostage drills!!!

I'd hate to be a hostage taker within your range!!!  NO WAY.  Wouldn't be too bad if I were the hostage though.  At least then I'd know that I'm taken care of rather than having some pissant cop who only shoots a shotgun once/twice a year for qualifications...

Next time I have to get a picture of your No-Hostage drill results.  It keeps the hostage taker's mind open to new things...    Wish I were that good with a shotgun.  I guess I need more practice.  

That is a popular way to load a 12 gauge in Bear country, 2 rounds of buck followed by 1 slug.  For home, pick the load that works best in your home, for me it is Buck.  I carry a few slugs in the saddle.

I have six 00Buck in the tube, three in the saddle, and three slugs in the saddle for bears/accuracy/hostage situations...whatver occurs in my house can be dealt with.  Probably not to many bear attacks down here though, but if there ever are, I got 'em!

Hi Mountainman8
faris has given you the lowdown.
I could reinforce some of the other observations made which are also valid.
In a HD situations slugs are very useful because of their precision over buckshot.  Some of this depends upon how well your shotgun patterns with various loads.  Really the best explanation of the proper use of the tactical shotgun that I've seen is Gunsite Training Academy's video, "Tactical Shotgun".  They cover all the stuff you need to know about the shotgun as a tactical weapon.  It's all very informative and interesting.  You can find this video on the web.  It only costs about twenty bucks.  It's the one with the yellow cover.