A solid state lamp, such as one that can replace an incandescent light bulb, has a base portion having an electrical connector for connection to a source of power, such as an Edison-type connector for connection to the mains voltage. An AC/DC converter in the base converts the mains voltage to a suitable light emitting diode (LED) drive voltage. A plurality of receptacles on the base connects to electrodes of plug-in modules. Each plug-in module supports a plurality of low power LEDs connected in series. The strings of LEDs on different modules are connected in parallel when connected to the receptacles. The modules and base are configured to allow a user to operate the lamp with different combinations of modules to generate a desired light output from the lamp. For example, the user can recreate the lumens equivalent of a 20 W, 40 W, or 60 W bulb by using one, two, or three modules.