Intel 945 motherboard supported processor
That is a socket LGA 755 motherboard and so it will fit the following processors, (copied from Wikipedia)
Intel Pentium 4 (2.60 - 3.80 GHz)
Intel Celeron D (2.53 - 3.60 GHz )
Intel Pentium 4 Extreme Edition (3.20 - 3.73 GHz)
Intel Pentium D (2.66 - 3.60 GHz)
Pentium Extreme Edition (3.20 - 3.73 GHz)
Pentium Dual-Core (1.40 - 3.33 GHz)
Intel Core 2 Duo (1.60 - 3.33 GHz)
Intel Core 2 Extreme (2.66 - 3.20 GHz)
Intel Core 2 Quad (2.33 - 3.00 GHz)
Intel Xeon (1.86-3.40 GHz)
Intel Celeron (1.60 - 2.40 GHz)
BUT (it is a huge but) I could find no support info from intel nor could I find any user posts that would narrow down which of those processors is actually supported by the Intel 945 motherboard. There is a possibility that some are not supported - although often a BIOS update will provide for support for later (now past) processors.
Summary: CPU's on the list will fit but support from mobo is unknown.