Oil filled radiator style are awesome! I have gotten one that had a defective cord that heated up however, so be aware you want to check that when you first get it. I've heard it can be an issue.
If you put it on a thermostat, it really is problem free, and I've put my clothing over it to warm up in the mornings in the winter. The clothing never gets so hot I'd worry, so I don't worry about fire hazards hardly at all with these.

Anything with exposed heating elements like the typical electric heaters with the coils that you can see getting red hot would be the least safe(not even counting the flame-making kerosine type heaters).