BIG SRAM with no parallel interface / SPI based?
You can get 512MB for $10 and they even throw in a complete ARM computer around it.

If you really want a serial RAM to retrofit on an existing board, the irony of modern ultra-mass-production is that it would probably be cheaper to stick the above ARM SBC with a little bit of code on it to emulate a serial RAM than to purchase the dedicated hardware device (if it even exists). And while you're at it, replace the existing micro with it...

If this is for DIY or low production volumes, 
I suggest you use such a module. Otherwise, there are Cortex-M4 or M3 micros with SDRAM interfaces, so you can simply add a cheap SDRAM chip.

The drawback of SDRAM and a big cpu is the higher power consumption versus SRAM and a slow cpu. If you absolutely need very low power, then that will be an issue. But SRAM is a lot more expensive and less available than SDRAM.

Here's another non-volatile option but also too small and expensive, although these non-volatile chips offer an interesting option: power draw is very low when not in use, because you can power them down!

What kind of speed and power do you need?

If this is for data logging, and the data throughput is low enough, the number of writes low enough, you could also use a SPI flash...