Except in certain specific scenarios, you should ALWAYS use resistors with LEDs. Without a resistor, you are stressing both the LED and the IC it's connected to (Arduino, shift register, etc). You're luck you didn't blow the LED or the IC (or both).
If your LEDs are too dim with a resistor, you have selected the wrong resistor. Use this website to find the appropriate value:
20mA is the typical maximum continuous current your average 5mm LED can handle. Coincidentally, that's also the recommended maximum for an Arduino pin.
The maximum for your shift register will vary, but it may be as low as 6mA, so you may require a larger value resistor. Check the datasheet.