Single faction and dual faction decks can both work quite well. More than 2 factions gets tricky because of resourcing issues. Note that some cards though are effectively colorless if they're cost 0 with no Steadfast or else have an ability that lets you put them into play (often temporarily) by spending resources of any color.
Single faction decks have the easiest time resourcing, can be more strongly themed, and can take more advantage of faction-specific Events/Supports. The drawback is a smaller card pool to draw on. Two factions = twice as many cards (minus the relatively few ones that no longer make sense).
Dual faction decks still work well from a resourcing perspective, although sometime you can get lopsided draws (mulligan helps). You can, to an extent, combine the strengths of both factions although you also frequently dilute them. For instance, a Cthulhu/Miskatonic deck is not as good at destroying stuff as a pure Cthulhu deck would be, but it gains Investigation and some tricks as compensation. Because dual faction decks give you twice the card pool, they're pretty much the default for players with small collections.
Some factions seem to be better equipped to run alone than others. Cthulhu for instance is well known for working well as a single faction, where Hastur or Miskatonic for instance have a little more trouble on their own. However, I expect once the new faction expansions are out the extra injection of cards will help a lot with this - Misatonic is the first one due out.