I want to know which processors are compatible with my laptop.

I have a Celeron M 440 1.86 GHz w/ the Mobile Intel® 940GML Express Chipset in my Acer Aspire 3680 Laptop.

Can I upgrade to a "Pentium" or "Core" type processor?

I'll say "no" based on the 940GML chipset's supported processor info at Mobile Intel® 940GML Express Chipset (http://ark.intel.com/chipset.aspx?familyID=24679) and Mobile Intel® 945 Express Chipset Family Datasheet (http://www.intel.com/Assets/PDF/datasheet/309219.pdf). Contact Acer (http://www.acerpanam.com) if in doubt.