SSR switches on under no load?

I have some 12A 240V SSRs with no data. I'm using them to switch a standard light bulb on and off. They work fine in my application, but what worries me is they seem to switch on when there is no load connected, even if there is no voltage to the input terminals.

For example, I have a 120V panel-mount indicator light wired up to the 120V switched side so that I can see when the SSR is switched on (I'm not sure if this indicator light is an incandescent or LED). With my load plugged in everything works fine and the panel indicator comes on when the SSR is switched and it goes off when it's not. But when I unplug the load, this panel indicator lights up as if the SSR is on. And if I measure the voltage at the receptacle, I get 120V as if the SSR was on, even though there is no voltage applied to the input terminals. When I plug the load back in, the indicator goes off and the light bulb does not light, unless voltage is applied to the switching terminals.

Why is it doing this? Do I need some kind of snubber/pulldown resistor somewhere, like across the input terminals or across the output terminals? Is this dangerous?

This is actually fairly normal for SSR's. SSR's are not relays and relays are not SSR's. They will often need a "minimum load" to operate. It's funny (well...interesting more than funny) to see people buy SSR's then use a DMM to measure the output terminal resistance when switched on and noting that it doesn't look like a "short".

So I would not worry. I don't think anything dangerous is going on. The SSR is just not expecting such a light current load as a panel indicator. As you noted, when you have a "real" load attached, it works fine.

-- The Ruggeduino: compatible with Arduino UNO, 24V operation, all I/O's fused and protected

Well, the behavior bothers me. How much load does the thing need to stay off? I wouldn't mind burning an 1/8 watt or so just to keep the panel indicator off when nothing is plugged in.

50kOhms of load across the output terminals was enough to get the SSR to stay off. I used 2 100kOhm resistors to get enough power handling.

How much load does the thing need to stay off?

The current flowing through the SSR when off is known as the leakage current. It is enough to give you an electric shock so remember it is not turned off. The resistor used as a load should be such that the leakage current flowing through it causes a voltage drop across it sufficiently small to be considered OFF by the normal load. Note it will never truly be off.