The Lego company tends to produce the highest quality parts, and should form the core of a collection. Their pieces are durable, have good apearance, and are perfectly uniform. They also have rights to several exciting themes (Star Wars, Harry Potter, Jurrasic Park) thus spurning interesting pieces and sets. Duplo bricks, the large bricks aimed at younger children, are even compatable with the smaller bricks -- a 2x2 brick fits onto a single Duplo bump. Similarly, a 2x2 Duplo fits onto a single Quatro bump. Unfortunately, the Lego company sometimes behaves monopalistically and often overprices its products, counting on branch loyalty to pull them through. Lego has been losing money in recent years but still controls a large market.
Megabloks, a Canadian brand that has been around almost as long as Legos, is highly compatable with Lego and demonstrates great innovation. The quality of their pieces varies with theme, but is overall worthwhile. The Probuilder sets are equal to Lego in appearance and quality, and are about a quarter the cost. The Blockbot theme is mostly specialized non-resuable pieces and are pretty low quality. I don't recommend them at all. The Dragon theme has great mini-figs and realistic trimmings, but the bricks themselves are of lower-than-average quality. They work fine on a small scale, but are slightly misaligned on a large scale, producing structural instability in large structures. However, the detailed knights and trolls are by far worth the price of the sets. Megablocks has been making profit in recent years, mostlty due to the Dragon sets.
Megabloks' micro or nano bricks do not follow in step. They are not compatable with either Legos or even regular Megabloks. They are almost a 3:2 ratio but don't quite work. This is a shame, since they are very cute.
Other brands sometimes pop up and fade away, and are usually good quality. For example, C3 (Marvel/DC comics), BTR (Transformers/GI Goe), and Blockmen (generic military) are/were all compatable. Get them while you can, since they never stay in business very long.
Beware of BestLock, which claims compatability with 'leading brands' but outright lies. Their brick/plate heights have a 5:4 (or is it 6:5?) ratio to Legos, making them hard to integrate. Worse, their holes do not fit snugly onto Lego bumps and fall off without any resistance (althought their bumps work fine with lego holes). They use extremely low quality plastic. The M16's their minifigs carry are Lego-compatable, and are the only redeeming feature. They have managed to hang around a couple of years despite this.