In one embodiment, an LED lamp has a generally bulb shape. The LEDs are low power types and are encapsulated in thin, narrow, flexible strips. The LEDs are connected in series in the strips to drop a desired voltage. The strips are affixed to the outer surface of a bulb form to provide structure to the lamp. The strips are connected in parallel to a power supply, which may be housed in the lamp. Since many low power LEDs are used and are spread out over a large surface area, there is no need for a large metal heat sink. Further, the light emission is similar to that of an incandescent bulb. In other embodiment, there is no bulb form and the strips are bendable to have a variety of shapes. In another embodiment, a light sheet is bent to provide 360 degrees of light emission. Many other embodiments are described.