House of Graphs: This is an excellent database of interesting graphs. Each entry includes a pile of invariant values, comments on the graph, often an image, and multiple ways to define the graph.
Pi-base: Topological examples. It reminds me of the book Counterexamples in Topology but higher-level and searchable.
Knot Atlas: Who doesn't love the Knot Atlas? If you want to know something about knots, or a particular knot, or just look at super-cool knot pictures, this is your place
polyDB: This gives a search-form interface to some collections of polytopes, mostly but not entirely objects of interest in algebraic and tropical geometry.
L-functions and modular forms database: This is broader than it sounds; in addition to databases of L-functions and modular forms, this site also has modular elliptic curves over the rationals, number fields, galois groups, characters of representations, information on the Riemann zeta function, and more.
Number field database: Results of computations on number fields.