While the thermodynamics of DNA hybridization is well understood, much less is known about the kinetics of this classic system. Filling this gap in our understanding has new urgency because DNA nanotechnology often depends critically on binding rates. Here we use a coarse-grained model to explore the hybridization kinetics of DNA oligomers, finding that strand association proceeds through a complex set of intermediate states. Successful binding events start with the formation of a few metastable base-pairing interactions, followed by zippering of the remaining bonds. However, despite reasonably strong interstrand interactions, initial contacts frequently fail to lead to zippering because the typical configurations in which they form differ from typical states of similar enthalpy in the double-stranded equilibrium ensemble. Therefore, if the association process is analyzed on the base-pair (secondary structure) level, it shows non-Markovian behavior. Initial contacts must be stabilized by two or three base pairs before full zippering is likely, resulting in negative effective activation enthalpies. Non-Arrhenius behavior is observed as the number of base pairs in the effective transition state increases with temperature. In addition, we find that alternative pathways involving misbonds can increase association rates. For repetitive sequences, misaligned duplexes frequently rearrange to form fully paired duplexes by two distinct processes which we label `pseudoknot' and `inchworm' internal displacement. We show how the above processes can explain why experimentally observed association rates of GC-rich oligomers are higher than rates of AT-rich equivalents. More generally, we argue that association rates can be modulated by sequence choice.