Should we trust a journal article that does not cite any previous work? My area of interest is not so well-researched in the US, but it attracts more interest in some developing countries where the topic is more relevant, but also where academic standards tend to be different, and I must proceed with much more caution.

In EBSCO, recently my searches have turned up a number of articles published in journals abroad that either: (1) contain no in-text citations, but present entries in the reference list related to material discussed earlier in the paper or (2) contain no citations at all and no reference list at the end.

Is the lack of citations in an article sufficient criteria for casting aside a paper, even if I think some of the ideas relate to a paper I am writing?
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.