What are some examples of coupled reactions in the cell?
All the anabolic reaction inside our body require energy. The majority of those reactions use the hydrolysis of ATP as source of energy. 

To cite a few reaction that require ATP:


Gluconeogenesis where 4 ATP, 2 GTP and 2 NADH2 are consume to produce glucose from pyruvate.
Formation of peptide bond between two amino acids.  Here the amino acid have to be first activate by binding to the tRNAc consuming ATP, as explain here (from wikipedia)


  Polymerization of amino acids is what creates proteins. This condensation reaction yields the newly formed peptide bond and a molecule of water. In cells, this reaction does not occur directly; instead, the amino acid is first activated by attachment to a transfer RNA molecule through an ester bond. This aminoacyl-tRNA is produced in an ATP-dependent reaction carried out by an aminoacyl tRNA synthetase

Ubiquitin ligase, that require ATP to activate ubiquitin for conjugaison and it transfer to an E2 enzyme. This pathway is mediate by the E1 enzyme, as suggested here


  There is one major E1 enzyme, shared by all ubiquitin ligases, that uses ATP to activate ubiquitin for conjugation and transfers it to an E2 enzyme. The E2 enzyme interacts with a specific E3 partner and transfers the ubiquitin to the target protein. 



Hope that it helps.