What is the best LBV you have used and why?

Never had one I liked, sorry...

What is a "Load-Bearing Vest"?

I have never used one that I have liked. They are either too movement restrictive or hold in too much heat. I'm sure there are good ones out there somewhere but I have sure haven't found one.

It's the vest that the military or SWAT teams use to carry their goodies: ammo, water, grenades, etc. If you ever catch Stargate, it's the black thing they all wear over their green uniform.

IMHO, based upon decades of poor fashion choices:
I believe that the load-bearing vest falls into the same general category as headlamps and protective eyewear: useful but too ugly/uncomforatble/geeky-looking to use in any but the worst possible conditions. But, I am a vest guy, married to a dw who tolerates my u/u/gl behaviors. Therefore I have some experience with the following:

Filson vests:
Several varieties, several pockets, durable enough to be part of your estate.
http://www.mnworkwear.com/Merchant2/merchant.mv?Screen=CTGY&Store_Code=MNW&Category_Code=FV

Safari photography/travel vests;
More pockets. geekier. cheaper. less durable, worn by journalists on assignment in Baghdad. looks good on them. Does not look good worn anywhere else.
http://walkabout.com/shop/coat-ff-vest.asp?gclid=CJrluO2XkpICFShMGgod6xRE_Q

Tactical vests:
Worn by LEO enforcing warrants and military personnel. looks good on them. Does not look good worn anywhere else.
http://www.tactical-store.com/ts-t5-tv-80001.html

Fishing vess:
Used by fisherman to carry equipment while wading. Tackle boxes tend to float way.looks good on them. Does not look good worn anywhere else.
http://www.sierratradingpost.com/d/204_Fishing-Vests-and-Jackets.html

Mountain/fleece/insulated vest.
Fashion accessories. People actually wear these in social circumstance.
http://www.cabelas.com/prod-1/0047901920565a.shtml

The theory is that vests store items for immediate access, and can be worn all the time. Rucks, fanny packs, briefcases and purses store things in a less accessible fashion, and are more likely to be separated from the user. One does not look sleek in a load-bearing vest, and one does looks like a 'person of interest' to leos in when they are worn out of their context.
The ideal container for survival equipment is probably a laptop computer case: lots of them around, lots of pockets, and they do not look threatening.
I have acquired each of these vets at one point or another, and have gotten actual use out of the first and last categories. Filson vests are suitable for business wear, and fleece/down vests for casual wear. Most can bear some load. Disclaimer: I have never sold a vest,and have no commercial interest in any of the vendors listed.

Do I ever agree with you there! It is also just my nature that I don't like to attract a lot of attention, whatever I'm doing, and a multi-pocket vest or usually ANY vest is not typical in public. I have too much closet space devoted to vests that "looked good" when I bought them, but they really have little use when in civilization for me. I wear them in the woods/fishing or at home. But you never know...30+ years ago when I was in school, carrying a backpack there would get you the same looks as wearing a multi-pocket vest today would...start a trend, maybe I'll live long enough to benefit from it!

"... Does not look good worn anywhere else..."

That pretty much says it all...

By LBV, I'm assuming you mean something more than just a safari/photo vest.

I like one that is as open as possible- what isn't pouches doesn't need to have material under it. But it also shouldn't LOOK tactical. Avoid anything that looks like it was worn on Stargate- unless it is halloween. Avoid black, avoid camo- OD, tan, coyote, foliage are the best bet. The fewer pockets, the better- a bunch of small pockets looks more "interesting" and one or two large ones on each side. Try to keep it as much as possible the same color, at least your pockets, with the straps a contrasting but close color if they they can't match, so they look like "trim".

My personal pick is the Tactical Tailor MAV. It can be swung around and worn as a lumbar pack- it becomes invisible at that point. And with a large pocket on each side, and a pair of small ones for pint water bottles, it looks almost like a fishing vest. Add fleece patches to the front of the large pockets, I doubt anyone who isn't a hard core gear junky would see it for what it is.

I really like the one made by http://www.dropzonetactical.com/ I really like the flexibility of it. Decent fell when you are wearing it or crawling around.