Parashurama, Lord Hanuman, Jambhavan and Lord Shiva appears in both(Ramayana and Mahabharata) What has been mentioned about Lord Rama in the Mahabharata?
In the Vana Parva of Mahabharata there is Ramopakhyana section ie. Ramayana is told there by Markandeya to Yudhisthira. One example from that section is:
"Markandeya said, 'O bull of the Bharata race, even Rama suffered unparalleled misery, for the evil-minded Ravana, king of the Rakshasas, having recourse to deceit and overpowering the vulture Jatayu, forcibly carried away his wife Sita from his asylum in the woods. Indeed, Rama, with the help of Sugriva, brought her back, constructing a bridge across the sea, and consuming Lanka with his keen-edged arrows.'
"Yudhishthira said, 'In what race was Rama born and what was the measure of his might and prowess? Whose son also was Ravana and for what was it that he had any misunderstanding with Rama? It behoveth thee, O illustrious one, to tell me all this in detail; for I long to hear the story of Rama of great achievements!'
"Markandeya said, 'Listen, O prince of Bharata's race, to this old history exactly as it happened! I will tell thee all about the distress suffered by Rama together with his wife. There was a great king named Aja sprung from me race of Ikshwaku. He had a son named Dasaratha who was devoted to the study of the Vedas and was ever pure. And Dasaratha had four sons conversant with morality and profit known by the names, respectively, of Rama, Lakshmana, Satrughna, and the mighty Bharata. And Rama had for his mother Kausalya, and Bharata had for his mother Kaikeyi, while those scourge of their enemies Lakshmana and Satrughna were the sons of Sumitra.
Discussing about Ram was well explained by @Tezz and @Ram in their answers. Here, I found another example how Ramayana is older than Mahabharata.
कर्मणैव हि संसिद्धिमास्थिता जनकादय: |
लोकसंग्रहमेवापि सम्पश्यन्कर्तुमर्हसि || Shlok 20, Chapter 3, Bhagavat Geeta.
Lord Krishna had given an example of king Janaka for how to attain a perfection through karma-yoga in ShrimatBhagvatgeeta.
Sri Krishna mentions Sri Rama (himself in previous avatara) in Bhagavad Gita 10.31