It's been discussed ad naseum on these boards but just to repeat the mantra, no authenticating company is 100% perfect.
That being said, JSA and PSA are at least the most widely accepted and respected (by most
) of the third party authenticators. So you are going to be reasonably safe.
But as Big Dave said, there are quite a few knowledgeable folks on this board so post a picture or a link to the item you are interested in and you'll get no shortage of opinions.