The title is self-explanatory, so let's start cooking...

1)  Make sure that PS4 is capable of true 1080 resolution.

2)  Make sure that PS4 is capable of true 3D technology.

3)  Make sure that PS4 is capable of true Motion Technology.

4)  Make sure that PS4 is backwards compatible with PS3.

5)  Make sure that PS2 and a selection of PS3 games are available for PS4 to download.

6)  Make sure that architecturally PS4 is compatible with PS3 (for various reasons).

7)  Make sure that PS4 is reasonably priced.

8)  Make sure that PS4 production efficiency is comparable to Wii now (rather than original Xbox!).

9)  Make sure that PS4 is not as chunky as PS3 (but rather as compact as PS1).

10) Make sure the Memory Capacities (RAM, HDD etc) have been greatly improved.

11) Make sure the Bluray transfer rates have been vastly improved.

12) Make sure that PS4 is power-efficient (rather than power hungry)

13) Make sure that PS4 is fully multi-tasking and fully functional internet-wise

Please feel free to add. None of those parts above imply that PS3 is incapable of any those features.

The PS4 should be BC all the way to the PS1.

I think a few must-haves would be an IR sensor so that universal remotes such as Logitech's Harmony remote will work with it, good launch titles that would ecompass the entire first year, and the biggest by far: PRICE. 

I personally have not purchased a Sony gaming system since PS1.  For the most part, I skipped the generation that included PS2, and Halo lured me away from PC and into the Xbox world. The 360 came out before the PS3, and with my Elder Scrolls addiction, it was a must buy for me at that time.  I have contemplated picking up a PS3 as well, however, until slim, it's price simply was too high for me to justify a purchase.  I do not have enough time to play the games that I already own, so it's main selling point to me is bluray, but with the costs of bluray movies being so stupidly high, it just isn't right for me. 

That said, I will say that I picked up a Wii once it came out.  Had I thought about it further, after the costs of buying 3 additional controllers nunchucks a memory card, I would've been better off purchasing a PS3 instead; oh well.  If the next system comes out with some compelling games and a good price point before I've already sunk entirely too much scratch into other systems, then, for gamers like myself, that will be the "right" formula.

1. Updated version of cell.

2. 1GB of XD RAM.

3. Improved Graphics Card

4. FULL Backwards Compatability

5. Standard 1080p graphics

6. Faster Blu-Ray drive.

7. Reliable hardware

8. Improved Operating System

I'm sure there are other important features or hardware specs but these are the ones that come to mind for me right now.

i want a gt game as a launch title, possibly gt6:P

but, but, they already started working on gt6, so why shoudnt its demo be ready in two years?

Business wise they need to sell it cheap on launch, around £100 more at max making it £350-ish. I expect they will focus on improving the 3D technology and I would like to see it, but this has to be done in conjunction with 3DTVs obviously.

I agree with more RAM, would be good.

In terms of B/C I expect there to be PS3 and maybe PS2, but not the PS1, they don't need to and would just cost more money.

I want it to stack easily, the curve on top makes it really difficult for storage.

DECENT LAUNCH GAMES. Resistance is an exception to the games they had.

As in the OP, increased bluray speed. Of course this is down to the BDA (which sony is in) and I think they are slowly getting there.

I expect they will do too much again with a hefty price tag, although probably not matching PS3. I just want Sony to be in profit from playstation so they buy even more dev studios so even more exclusives.

Simples, have Naughty Dog make a launch game, and then everything will be fine

Make sure that all the games you downloaded off the PSN in the PS3 are completely transfable to the PS4.

Make sure that we share the same trophy system and that our PS3 trophies are as compatible to the PS4.

Actually the most important thing for the PS4 is to put in hardware features that makes giving the PS3 version fo a multiplatform game the edge super easy for developers, like 'free' AA or more RAM than the competition.