I don't know which CPU models you are referring to but the link below has a current generation CPU for each of those series.
http://ark.intel.com/compare/77769,77777,76344
The most recent Core i3 and Pentium CPUs are based on the current generation Haswell core. Celeron CPUs with the Haswell core has not been released yet so the most recent models are based on the older Ivy Bridge core. At the same clockspeed, Haswell cores are 6% more powerful than Ivy Bridge cores.
The i3 series has Hyper Threading, but the others do not. From a gaming perspective HT is not really used. The exception is Battlefield 4 multiplayer mode where performance charts does prove that HT in the Core i3 CPU are being used at close to 100% capacity. However, BF 4 is the exception. However, other programs you use might take advantage of HT like file compression / decompression. Video encoding can also benefit assuming the video codec and the encoding program can both make use of HT.
The core i3 has the most cache while Celeron has the least. I don't think it matters too much for games. But more never hurts.
Celeron only supports DDR3-1333 RAM while the other supports up to DDR3-1600. This can affect game performance a little bit.
If you are relying on the integrated graphics core to play games, then you definitely want the Core i3 CPU.