During the famous Car Festival or the Rath Yatra of Puri, Lord Shiva(here seen in form of "Hari Hara") is worshiped as one of the nine presiding Deities(Parsva Devatas) of the Chariot of Lord Jagannath named Nandighosha.

This fabulous pic of Hari Hara with the following passage:

During the famous Car Festival or the Rath Yatra of Puri, Lord Shiva(here seen in form of "Hari Hara") is worshiped as one of the nine presiding Deities(Parsva Devatas) of the Chariot of Lord Jagannath named Nandighosha. It is made up of wood like the idol of Lord Jagannath and is placed by the side(parsva) of the Chariot. While after the completion of Rath Yatra, the Chariots are dismantled, the presiding deities remain intact and are only replaced with new idols during the Navakalevara(which falls roughly around every 12 years) alongwith the main wooden deities of Lord Jagannath, Balabhadra, Subhadra and Sudarshan.
It is to be noted that Lord Jagannath is also worshiped as Bhairav(A form of Lord Shiva) in Sri Jagannath Temple(Sri Mandir) of Puri. Goddess Vimala is worshiped as Bhairavi. The Prasad of Lord Jagannath is called Mahaprasad only after it is offered to Goddess Vimala.
The three Deities of the Sri Jagannath Temple of Puri (Sri Mandir) are adorned with specific ceremonial costumes on various occasions. These are called as “Vesas” of the Lord. These Vesas are related to divine activities of Lord Krishna (as described in Srimad Bhagavata Mahapurana), Lord Rama (as described in Ramayana) and also to the five cults of Hinduism (Shaiva, Shakta, Vaishnava, Saura and Ganapatya). Interestingly the only Vesa of the Deities that is related to Shaivism is called as "Hari Hara" Vesa where Lord Balabhadra is decorated as Hari Hara(Half Vishnu & Half Shiva). Lord Balabhadra(incarnation of Sri Balaram) is worshiped as the elder brother of Lord Jagannath(incarnation of Sri Krishna) and is attributed with the qualities of Lord Shiva and his wooden idol is painted in white color which is the color of Lord Shiva.
Since the origin of the Vaishnava and Shaiva cult, there has been differences between these two cults regarding the supremacy of one over the other. But in order to clarify this doubt Lord Shiva took "Hari Hara" form to prove to the devotees that both Him and Lord Vishnu are the same.
It is rightly said -
"Yo rudrah sa swayam vishnu yo vishnuh sa mahesvarah
Ubhayorantarang nasti pavanakashambhoriva"
He, who is Rudra is also Vishnu and He, who is Vishnu is also Mahesvara. Just like there is no difference between Vayu(air) and Akash(Ether or space), similarly there is no difference between these two Gods.
Hariharaya Namo Namah !!