Is 2960 / 2960-X a layer 3 switch?

Maybe you will answer NO immediately.  That is my understanding before too!  However recently I've found out this is not the case!  I have my old 2960 PD 8-port compact switch, upgraded with 15.0(2)SE6 LAN Base image and make it "routable"!  All you need to do is, change the SDM template, using the command "sdm prefer lanbase-default" and reboot it.  After that you will be able to configure SVI with IP addresses, as well as configure static routes and default gateway on that switches.  I have tried 2960-X and it resulted the same.  Just need to make sure you are using the LAN Base version of IOS, not LAN Lite as LAN Lite doesn't have this capability.  

More info here:

http://www.cisco.com/c/en/us/td/docs/switches/lan/catalyst2960x/software/15-0_2_EX/routing/configuration_guide/b_rt_152ex_2960-x_cg/b_rt_152ex_2960-x_cg_chapter_010.html