I just purchased an intel core duo processor. When games give minimum processing speed requirements, does that apply for duo processors? (ie can I play a game that requires a 3 ghz intel processor on my 1.8 ghz duo processor)?
Core Duo, or Core 2 Duo? Performance for games is going to be faster on the latter.
Those speed estimates have generally been given for a Pentium 4 (or their close relatives); as a rule of thumb, AMD and Intel chips of the Pentium-M/Core Duo (not Core 2 Duo) are equivalent to a Pentium 4 of around 50% faster clock speed - one core of a 1.8ghz Core Duo is going to be /around/ the same speed as a 2.7ghz Pentium 4.
So it might be a little slow for a game designed for a 3ghz processor but not bad. Odds are it'll be playable, but not great.
Now, if it's a Core 2 Duo, you should be fine. Core 2 Duo at least 10% faster than AMD/Pentium M/Core Duo. So a 1.8ghz Core 2 Duo would be around as fast as a 3ghz P4. In my experience, my Core 2 Duo 2.0ghz laptop is around the same processor speed as my 3.4ghz Pentium D (dual core Pentium 4) desktop, maybe even a little faster for things like converting video files.
Now, the dual core/single core is a separate issue - as Eponym noted, until recently, most games were written to run in a single thread. So it's the speed of a single core that matters (although you'll get some *small* advantage from the second core doing some of the extra work for Windows regardless.)
I'm not sure what LifetimeDoc meant by "it's more like you have two 900Mhz processors that work more efficiently than a 1.8Ghz single core processor" - a 1.8ghz Core Duo/Core 2 Duo is two cores each running at 1.8ghz. No matter what, there's no speed lost by going to dual core at a given clock speed.
Two other things to note:
1) for games, the video card is going to often matter more than the processor, which is why I still mostly play games on my desktop.
2) The speed of your front-side-bus and memory matters a good bit. Two processors of the same architacture generation running at the same clock speed but with front-side-bus speeds that are different (or if one is slowed down by memory slower than the FSB) can have very different performance characteristics. This was most evident back with the P4 where the third versions of the 2.4ghz chip was nearly twice as fast as the first(*), but it's still the main reason today why desktop chips are faster than laptops.
(* The P4 was a very memory-bandwidth-intensive design, and the speed of the FSB went up twice from the original 400mhz to 533mhz to 800mhz - with the same clock speed of 2.4ghz. At the same time, they also introduced dual-channel memory with the 800mhz-capable motherboards so the total bandwidth quadrupled.)