In no particular order:

• Gaussian Unitary Ensemble and Gaussian Orthogonal Ensemble matrices
• Yang Mills quantum gravity
• Galton Watston trees
• First and last passage percolation
• The Ising Model
• Uniform spanning tree
• The Airy process
• Determinental point process
• Schramm Loewner evolution
• The voter model
• (Totally) asymmetric simple exclusion process
• Gaussian free fields
• Random walks in random environments
• Liouville Quantum Gravity
• The Brownian map
• Random graphs