Should we trust a journal article that does not cite any previous work?
I think it depends what you mean by "trust".  

A modern academic paper which references no other paper is unusual and possibly fishy, but at least in my field (mathematics) there is nothing inherently faulty about the practice: perhaps you really are answering a question that you thought up yourself and for which the answer does not require you to use or cause you to refer to any published result.  (There must be some examples of this: anyone?)  

If you're being asked to evaluate a paper then, sure, read it much more carefully if there are no citations.  That's not a good sign.  If you know the field well enough to know specific papers that the paper you're reading should have cited, then you should evaluate the paper negatively for not citing them.  If the paper has been published in a reputable journal you might consider writing to the editors to suggest missed citations.  

On the other hand, a lack of references (or in-line citations) does not cause a paper to cease to exist.  If you want to cite the paper then you still can, and if you do use the material in the paper then you must cite it, as usual.