I'm looking more for major shifts in approaches to analyses that arose from bioinformatic development or borrowed from related fields rather than those borne strictly in response to new wet lab techniques
Some examples I can think of...
- kmer and graph-based methods to genome assembly
- reference-free, pseudoalignments for transcript quantification
- emergence of pipeline frameworks as standard practice
- deep learning methods applied to variant calling
- application of manifold learning/nonlinear dimensionality reduction to visualization (e.g. tSNE)