[A version of this post first appeared on SynTAROTis]
There are good arguments both for using reversals and for ignoring them. If you are a beginner, you might choose to ignore them at first, simply turning a reversed card upright. The upright cards are complicated enough on their own!
Each card in the tarot deck has a whole range of meanings, from one extreme to another. Mary K Greer, in her fantastic book Mary K. Greer's 21 ways to read a Tarot card, has a section on how to work with ranges of meaning. When you take the full spectrum of meaning for each card into account, working with reversals is unnecessary.
In Tarot tells the tale: Explore three-card readings through familiar stories, James Ricklef gives even more ways to read a reversed card.
You could look at a reversed card as one that draws attention to itself, or to one of the reversed meanings that can be applied—the opposite of the upright meaning, or more inward-looking or private meaning, or as blocked energy.
If you have a card in a "blockage" position (e.g. where the position in the spread is called something like crossing, inhibitions, obstacles, or blockage), you might find that the reversed meaning of the card given by the accompanying book or pamphlet holds a clue, even if you do not use reversals as a rule.
For a positive card in a difficult position, say the Sun in a "what to avoid" position, you could also look to reversed meanings for an interpretation.
If you want to use reversals when you are reading for someone else, you could start by explaining what the card means in an upright position. Before you go on to the reversed meaning, the querent may already have given you an idea what the reversed card could mean. She or he might say "I wish ..." or "I have always wanted ...", pointing to a lack, a block etc.
Personally, I prefer to use reversals, especially when I'm interpreting a spread for myself. I simply want to know quite clearly whether one or the other side of a spectrum should be emphasised for the specific card in that specific position, just in case I'm tempted to ignore certain warnings or vices that the card could point to. Of course, if I'm really honest with myself, I wouldn't be tempted—but just in case!