See http://pga.lbl.gov/Workshop/April2002/lectures/Olken.pdf for details, in brief:
• Continuous characters, lots of data, few computing resources ==> Neighbor joining
• Discrete characters, few mutations / homoplasy ==> Maximum Parsimony
• Discrete characters, limited sequence lengths, some homoplasy ==> Maximum Likelihood Estimation
• Discrete characters, many taxa ==> Supertree
• Complete genomes ==> Whole genome phylogeny