What Can I Do With This LPS?

Since it has one rail that is 12-15VDC, that should be very flexible for a number of things. A router, satellite, or ethernet switch is one area. If you use a NAS or server/streamer that uses a typical wall wart, that might be a good area for an upgrade. Even some DACs can benefit if they use a wall wart. That said, just make sure whatever you are trying to power uses a voltage rating that matches your power supply. 

You should make sure the voltage requirements are aligned with the rails of the power supply. Sometimes a unit can be flexible (EtherRegen can use 7v-12v for instance), but in most cases it needs a specific voltage and ampere. The voltage should be listed on the wall wart you are replacing, on the unit itself, or in its manual.

Amperes are also important, but they do not need to be matched. The ampere rating is the amount of current that the power supply can handle. It can be higher than the unit you are trying to power, but not lower. If the unit you are trying to power requires more amperage than the power supply can provide, it will fry the fuse in the power supply, or the fry the power supply itself. The wall warts that you are replacing may have a higher ampere rating than the unit actually draws. It is more important to know what the unit requires vs trying to match the wall wart.