Hallo Mikkel,

you wrote:

Isn't that only when they work fast? If you use a fast SRAM chip in a "slow" circuit will it actually consume more power?

You are right. Power consumption is often measured in combination with certain toggling rate of enable line. So, when using a fast SRAM with 'slow' circuit much lower power consumption will be observed. It's neccessary to have a look at actual datasheet to find out, how much this access rate influences total power consumption.

Why is power consumption increased with higher access rates?
This is a typical behaviour of CMOS! Whenever logic states are changed, internal stray capacitance, gate source capacitance, etc. has to be charged or discharged. The according current flows only for a very short time and results in a heavy spike!!
In order to achieve fast switching, time to charge or discharge stray capacitance must be decreased. But if the same amount of charge has to be moved, according to Q = I x t, current spike is higher. Of course, manufacturer do everything to make internal stray capacitance smaller and smaller, and to develop 'clean' designs (charge injection compensation, etc). But fact is, that faster CMOS chips still today often produce higher current spikes. So, even in 'slow' circuits a faster SRAM will mostly produce a higher current spike, when being enabled.
Without mentioning that this can cause an overall increase of supply current, a higher current spike is always dangerous of course! Think about difference of 74HCMOS and 74ACMOS for instance. A simple PCB without solid ground plane and rather poor power supply decoupling measures may work with HCMOS, but when switching to ACMOS, often a desaster results.
So, it's always wise to use as slow chips as possible. But this does of course not mean, that's impossible to use a fast SRAM, as you did...

I have used cache chips (20ns) as RAM in 8051 applications without problems. Perhaps I have just been lucky?

Or may be I'm too paranoid? If you are a professional and one wrong decision can ruin your company you become a bit carefull....
Joke aside, if you have a proper design and can live with an eventually increased current consumption, than nothing speaks against this fast SRAM. But if you toy with a bread board this wouldn't be a good idea at all!

Regards,
Kai