Algorithms that must compute a global property?
A silly example: Checking if a graph has more than m nodes. :-)
Some more interesting examples:

Checking if a graph is connected.
Checking if a graph has an Eulerian cycle. A graph is Eulerian iff all degrees are even and the graph is connected: https://en.wikipedia.org/wiki/Eulerian_path
Checking if a graph has a perfect matching: https://en.wikipedia.org/wiki/Blossom_algorithm