Over the years, we've bought mostly Legos because of their quality and variety and number of kits. We have a few Megablocks from Canada, my son is a big fan of Pirates of the Caribbean and MegaBlocks got the contract to make constuction kits for the franchise. A few years ago we spotted some Kids Connection bricks at Wal-Mart, they were extremely cheap and in a neat storage case, so we snatched them up. I've recently discovered another company, Best-Lock out of England.
Legos are to found everywhere. Kids Connection is a brand owned by Wal-Mart, so they're exclusive, but they look a lot like MegaBlocks, so I bet MegaBlocks makes them for Wal-Mart and several other retailers. Mega-Blocks are found everywhere. Toys'R'Us has Best-Lock on their shelves and on their amazon.com portal.
I'm sure there are a dozen different companies that copy Legos or come into their own, these are just the name brands that I've come into contact with.
I just found out that K'NEX also makes good quality bricks that are compatible with Legos, but we don't have any K'NEX bricks, just the sticks and connectors. (thanks westfw!)
Step 1: Lego my construction brick!
They are made of relatively dense plastic and very opaque. They usually have very little flash on their pieces. The denser plastic also makes for better adhesion. If the bricks make a sharp click when they stick together, they're going to be harder to seperate. (Thanks for the reminder, LilPunk32!) Legos almost always click, and some times require the use of the Lego Brick Seperator tool. The tool comes in handy when dealing with flat plates that require leverage.
You can order all sorts of bricks on-line at lego.com through their "Pick-A-Brick" program. You can also order any piece from any set over the phone, but it'll cost ya, they have to ship them from their headquarters in Denmark.
Step 2: Best-Lock
They click perfectly with Legos and make a perfect substitute. They are also significantly cheaper, but they don't have as much of a variety of specialized bricks as Lego. I had to use a knife to take a misplaced plate off my son's pirate ship last night, so they stick as well as Lego bricks.
They lack the support ribs that the Legos have. That shouldn't be a problem, unless you're going to make a piece of furniture out of them.
Step 3: MegaBlocks
Their pieces are made of a lighter density plastic than Lego or Best-Lock bricks, so they don't click like Lego bricks and they are easy to come apart. They are noticeably paler in tone and less opaque than Lego or Best-Lock bricks. They also show some flash from the sprue. They have a raised edge on one of the studs where the sprue was attached. They have "MegaBlocks" written in raised lettering on one of the studs.
Step 4: Kids Connection storebrand
The plastic is identical in density and opacity to the MegaBlocks, as well as adherance, they "thud" more than "click" and come apart easily. The bricks are so soft, you can actually squeeze the larger ones with your fingers. The bricks also have a raised edge on the stud where the sprue was attached, just like MegaBlocks. They just don't have any identifying marks. I assume they are made by MegaBlocks for the different chains, but don't hold me to that.
Step 5: All together now
If you need cheap basic shaped bricks but don't care about their color or opacity, any of the four will do. If you need a higher density brick, that will stick together, I would go with Lego or Best-Lock.