What is the minimum separation for navaids to work properly without interfering?
VOR/DME and NDBs can't interfere with each other: they work on completely different wavelengths, so you could have a VOR right next to an NDB and they'll work just fine. Similarly, VORs on different frequencies won't interfere with each other; you could have them in close proximity as well. The only time you are likely to see navaids in close proximity is at an airport, which may have an NDB, VOR/DME, and multiple ILS in operation (an airport with 2 airstrips may have 4 ILS in operation: 1 per runway). 

Where you do get interference is when stations are using the same frequency. A VOR has a service volume, a set distance it is designed to reach; in the US the high altitude service area is a minimum of 130 nautical miles at 45,000ft, but in practice in the right conditions you can pick them up further than that. Some stations are set at a lower power and have less range.