Desktop

No problem what so ever. In fact, if you do any over-clocking, then that is even better.

Speed wise, SDRAM DIMMs are fully backwards compatible.

You can use PC133 DIMMs on a PC66 system.

The problem that you may run into using newer RAM on older systems is that the SDRAM DIMM specification has evolved over time.
Many older motherboards cannot address the newer quad density SDRAM DIMMs.

Also, be mindful of any memory field size limits for your motherboard.
I've seen motherboards that limit DIMM size to 32MB, 64MB, 128MB, and even socket by socket DIMM limits.

Chas

It depends.

I have seen systems with mismatched SDRAM not booting at all.
I have seen systems not recognizing full RAM size. A 128MB RAM can be recognized only a portion of it, like 64 MB. I have even seen a 64MB being recognized as 16MB.
I have seen a system (PIII 1GHz / 133Mhz clock speed) would take an old PC133 256MB SDRAM but not newer PC133 256MB.

In general, it is a good practice to keep the SDRAM as close as possible to the CPU clock speed.
It is the most efficient for the system if the speeds of CPU, MB (FSB), and the RAM synchronize.