Hi Mike,
GA these days is a last resort, since IV sedation is so much safer and has the same effect as GA in about 98% of people with a dental phobia (that estimate comes from Stanley Malamed's book on sedation in dentistry).
IV sedation is useful if someone really doesn't want to know what is going on, and if they're really afraid of certain dental procedures. It is also useful for stuff which almost anyone would find unpleasant (like a lot of teeth being removed in one go, or difficult-to-remove teeth like impacted wisdom teeth), and for people who have difficulties with an extreme gag reflex, especially if it's physiologically caused rather than a psychological reaction.
RA (nitrous oxide) is a more participatory technique and perhaps better suited to people who like to be in control, but who want something that takes the edge of their anxiety.
Then of course there are many psychological techniques which can be used - many of them originated from children's dentistry like tell-show-do, structured time, giving lots of control to the patient, using non-threatening language, etc. These can work really well for lots of people with dental fears, and unfortunately they're a bit underused in some regions due to the relatively wide availability of sedation options these days.
GA is rarely called for these days - basically only if IV sedation doesn't work for whatever reason in a particularly phobic person. For example, if the person has a very high tolerance to the drugs used for IV sedation (benzodiazepines) due to long-term use - in that case, IV sedation doesn't always have the desired effect.