SONYs Original Plan was to incorporate both the PS2s Emotion Engine chip and Graphics Synthesizer CPU chip on to the PS3 chipset for full Hardware Backwoods Compatibility just like the PS2 did with the PS1 . all 20GB and 60GB Japanese Spec and US Spec models had both the Emotion Engine CPU and the Graphics Synthesizer GPU incorporated in them but the Korean Spec 80GB models and Euro Spec 60GB models and first batch of 80GB US Spec models had the Emotion Engine CPU chip removed but still had the PS2s Graphics Synthesizer GPU with software emulation used for Emotion Engine reducing the number of compatible PS2 titles. all 40GB, 160GB had no PS2 hardware incorporated in them and all 80GB FAT medals made after the Limited Edition  MGS4 Gunmetal Gary model had no PS2 hardware incorporated in the as well as all PS3 slim models. 

all Backwoods compatible models allso have the ability to make unlimited numbers of virtual PS1 & PS2 memory cards and upscale the output of PS1 & PS2 Games to 1080i though the HDMI output all there is as graphics smoothing filter as well.

I have the Original Japanese 60GB model that I imported back in December 2006 the only problem is that even though all PS3 games are Regine Free all PS1 and PS2 games are restricted to NTSC-J. but I will be buying a Japanese PS2 just incase my PS3 dies.

I believe that SONY should have found a way of keeping the PS2 hardware incorporated in the PS3 because it most likely cost them some sales and would would have persuaded more PS2 fans to migrate to the PS3 earlier.             

http://en.wikipedia.org/wiki/PlayStation_3

Otherwise you wouldn't buy the HD collections of GoW, Sly, Team Ico etc?

Do people still want PS2 BC about 4yrs in the PS3's life span. I have a 60GB PS3 and I have never bought a ps2 game. lol

It is ironic that that the original XBOX had a custom Nvidia GF3 GPU without ED-RAM and the PS2 had ED-RAM and the PS3s RSX GPU based on the G70/71 chip amounting to something in-between a 7800GTX and 7900GTX with out ED-RAM and the XBOX 360 custom ATI R520 chip essentially a 1900XT GPU with ED-RAM.    

it is so we can play are PS2 collections through HDMI and upscaled to 1080i. and all PS2s have full PS1 B/C so way should the PS3 not have PS1 and PS2 B/c as well.  

I have the 80gb PS3 b/c SKU but maybe i havent played alot of PS2 games on there but the ones that i have played didnt show any issues of how the video described running on my PS3.

Yeah there's more problem with the 80GB version. Jak and Daxter doesn't work on my MGS4 one.

You just have to compare on this site:

http://us.playstation.com/support/compatiblestatus/

To do proper hardware emulation in software you tend to need dramatically more processing power because you're (effectively) running a full simulation of the hardware ... Years ago I was given estimates that it took 10 to 20 times the processing power of systems like the Colecovision, Atari, NES, SNES and Genesis to properly emulate the hardware.

There are other ways to emulate hardware, and the most common alternative is instruction translation; which effectively works by converting an instruction from one architecture to another architecture; and then only doing a full emulation on the instructions that can't be translated. Since many/most of the instructions in one architecture operate differently than the instructions in another architecture, instruction translation tends to be very buggy.

You can follow a hybrid approach, and maintain a database of games with the instructions they need to be fully emulated in software but this is a time consuming and expensive approach.

Regardless of the hype, the PS3 is simply not powerful enough to fully emulate the PS2 and Sony was forced to use instruction translation when they eliminated the emotion engine to cut costs; and they had no desire to cover the costs of creating a database of thousands of games with the "settings" to make the game run well.

Just to clear up what some people don't seem to fully understand:
For the US-

Launch 60/20GB; Full B/C Emotion Engine (PS2 CPU) and Graphics Synthesizer (PS2 GPU)
80GB (4 USB ports) Launched in Aug07 in Motorstorm Bundle and later relaunched as an MGS4 bundle; Graphics Synthesizer (PS2 GPU), No Emotion Engine (Emulated by the Cell)
40GB Launched in Oct07 and every model after except the minor return of the above mentioned 80 for MGS4; No EE or GS chips

For EU-

Launch 60; Same as first 80GB
Later models; Same as 40GB mentioned above

It's worth noting that throughout firmware updates, PS3's that were emulating the cell had gradually improving B/C support.

As for why SONY can't simply emulate both chips? See HappySqurriel's post. Last I checked the best PS2 emulater out there required 2GB of ram and prior the best required 4GB. We're talking about emulating a system that only had 32MB of ram TOTAL.

They could always get the Open Source Code for PCSX2 and tailor it specifically to the PS3, it's more than powerful enough to handle it if they change the code to specifically work on the PS3 hardware, but they'll prolly never do that.