Most likely 16GB. Samsung is already shipping their 16Gb (small 'b') GDDR6 chips to NVIDIA now for the GeForce RTX cards. These are doubled in capacity from 8Gb chips used in the PS4 and Xbox One. So, for PS5, Sony could use the same amount of chips as they are now, but just 16Gb GDDR6 ones, for a doubling of both memory bandwidth and capacity. This wouldn't even increase costs - the 16Gb chips have a premium now since GDDR6 itself is new, but that premium will be gone before PS5 arrives.

However, ONLY getting double the memory bandwidth on a 256-bit bus is kind of the absolute bare minimum Sony should do. They should really move to 16Gb GDDR6 chips AND a 384-bit bus, ala Xbox One X, which would bring the total to 24GB of memory. That would also bring the system to 672GB/sec of bandwidth using the bargain-basement 14Gbps GDDR6 speed. Yes, I said bargain-basement - it may be state-of-the-art right now in the GeForce RTX series, but 14Gbps is the minimum GDDR6 official speed. By 2020 when PS5 releases, NVIDIA and AMD will be on 18 and 20Gbps, and the 14Gbps will be used for the budget cards.

Depends on time of release. I'd guess some 17 to 18 GB, with 1-2GB dedicated to system functions and background tasks.

A later release could lead to 33-36GB with 1-3GB reserved for system operations. I don't expect this gen to go on as long as the last.

Also
PS1 2MB RAM (system)+ 1MB VRAM
PS2 32MB RDRAM (system)+ 4MB eDRAM
PS3 256MB XDR (system)+ 256MB GDDR3
PS4 8GDDR5 (unified)+ 256MB DDR3 (for background task)

EDITED.

http://www.redgamingtech.com/ps4-developers-were-speechless-when-8gb-gddr5-ram-was-announced/

https://www.videogamer.com/news/ps4s-8gb-ram-was-kept-secret-from-third-party-devs-until-console-reveal

128 GB maybe in PS7.

Dont know. Dont care.
Im curious on what Sony is doing next software wise.

They can fit 8gb RAM in a mobile phone 

It's going to be 32GB using clamshell mode. Same number of chips of the original PS4 (16), 8 on each sides of the motherboard.

My computer runs fine with 8gb ram + 3.5+.05 VRAM.

Edit: Changing my answer to 16 or 24

He is talking pricewise. It amazes me that people say that mobile phones now have 8GB so that automatically means that console will have a lot more than that... Have you seen the price of those mobile phones?, the ones that have that amount of ram?

Prices of phones have skyrocketed in last couple of years. So if your fine with consoles being 700-800+ dollars with 32GB, which doesn't even make sense, because the hardware wont be able to use all that RAM.... Of course you can load everything to ram but thats just a stupid use of it and wont translate into any appreciable gains... When you are not constrained by ram, having more ram just doesn't make sense... ram is not the holy grail and it's really expensive these days.

I think 16GB is more than enough and personally cant see it going over 24GB which is already kinda overkill for gaming.

Hmm... this is what I thought but then I saw everyone going to 32GB and I felt stupid. Now I'm conflicted again. I always thought 16 sounded right. But idk. 

A higher ESRam buffer will be used along with higher bus 16gb GDDR5