Most elements will have their official "Design ID" imprinted on them - this is typically the longer number, and can usually be used on the Pick a Brick site or sites such as BrickLink and Peeron to track down additional bricks. Note that this is different to the "Element ID" that is printed in the instruction part inventories which has the colour encoded with it.
I've got the following three elements in front of me at the moment:
The 6x2 plate [part:3795:6] has the following:
- © LEGO (highlighted in red)
- 03795 - This is the padded Design ID (highlighted in blue)
- 10 049 (highlighted in yellow)
The 4x1 tile [part:2431:6] has the following:
- © LEGO (red)
- 2431 - This is the Design ID (blue)
- 15-10 (yellow) - 3 others in the same set had different numbers
The Plant Leaves 4x3 [part:2423:2] has the following:
- © LEGO Group (red)
- 2423 - This is the Design ID (blue)
- 6•02 (yellow) - another one of these in the same set had the same number.
I believe the numbers highlighted in yellow are mould numbers - so the factories can track down imperfections with old moulds or similar.
Looking at an element that I have in rather large quantities now, the Tile 4 x 3 with 4 Studs in Centre [part:88646:0] taking four at random they all have:
- © 2009 The LEGO Group
But then each one has a different mould ID:
With regards to the copyright statement - as you can see across from these examples, they use different versions depending on the space available. I guess they feel that having the part and mould ids are slightly more important than their copyright statement for tracking purposes.