Op-amps that get really close to the supply voltage
What you want is called a rail-to-rail op-amp. Digikey lets you narrow by that as a parameter, under "Output Type". Some of the more common ones in the package you want include:
LMC662
TS912
LMV358
MCP6002

I've personally made good use of MCP6002 in a DIP8 package.