The answer depends on what games you play. If a game supports multi-core processors (which many older games do not) then quite often it's still limited to 2 cores anyway due to their programming, so a quad core processor won't necessarily bring about greater performance, especially if it is lower clocked than the dual core one. The list of games that would use all 4 cores of a quad core processor is surprisingly small. However, as time passes, more and more games are programmed to start using more cores, so if you intend to keep buying brand new PC games then a quad core will provide more future proofing.
One thing you may want to consider is if a processor upgrade is really going to affect performance that much anyway. With a core 2 duo, it's more likely most of your games are limited by your graphics card than the processor (there are exceptions, with the TW series being one as it seems very processor intensive). One further thing to consider is if you wouldn't be better off upgrading your motherboard and processor at the same time. The new Sandybridge processors are light years ahead of the old core 2 duo's in terms of performance, so it may be cheaper and provide a bigger performance boost to buy a new motherboard and a less powerful Sandybridge processor than it would to buy an older, higher range core 2 processor, although more effort on your part to replace your motherboard.
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