Is it safe to look at infrared LEDs?
Infrared wavelengths are EM waves of longer wavelengths than visible light. Also, visible waves are more energetic than IR waves.

Because of this, Visible light has the ability to excite organic receptor molecules in our eyes called Rods and Cones. These molecules stimulate cell responses and in turn excite cell responses in our nerves called an Action Response. Still unclear to most scientists is how the brain composes these action responses into an image, though a great deal of research is being done to date.

The reason why "nothing happens" when we aim infrared lights into our eyes (which I still wouldn't suggest) is that the photoreceptor molecules that we use to see don't have the necessary bonding configuration to accept the energy from these impinging EM waves.
 However, don't go thinking that nothing happens. Infrared radiation is a type of radiation that is usually a measurable heat source. IR is one of the broader parts of the EM spectrum. My point is to say, that when you "radiate" some thing with an IR source:
1) You don't know if it is also radiating other EM waves unless you know the specs. 
2) You're still exciting molecules with that energy even if it isn't causing a seen effect. I highly doubt anything will happen unless you have a very high powered IR source. You shouldn't really ever focus high power lasers of any source onto your body, because higher intensities could inflict damage.

To Learn more about IR radiation:
http://coolcosmos.ipac.caltech.edu/cosmic_classroom/ask_astronomer/faq/radiation.shtml

IR (InfraRed) 
EM (ElectroMagnetic)