Well, if we go all the way back to the predecessor of the Mughal Empire (the Timurid Empire), the two states despised one another. The eponymous Timur was responsible for breaking the Ottomans at Ankara (their sultan died in captivity and then his sons started a civil war). The decline of the Timurids prevented that feud from going any further; border territory was ceded or lost to Turcoman tribes (Aq Qoyunlu and Qara Qoyunlu), who fought amongst themselves, before the eventual rise of Shah Ismail I, who went on found Persia (which would, of course, be a perennial Ottoman rival).

But the Mughals were a different matter. Territorial disputes were no longer on the table; the Timurid dynasty no longer claimed hegemony (there was a period in the early 15th century when Ottoman claimants to the throne were reluctant to mint coins or call themselves sultan) and the two powers found common cause on a number of issues. They were both Islamic dynasties ruling over religiously diverse empires and they both faced the threat of an ever-encroaching Portuguese presence in the Indian Ocean. We see the Mughals invite dervish orders into their territories, spend huge quantities of gold on the hajj trade, and merchants from Mughal territories did their business as far afield as Aleppo and Alexandria (this during a time when the Ottomans frequently seized the assets of foreign traders and resettled them in Rumelia, as rather infamously happened to Persian merchants at Bursa).

Over time, these cordial relations evolved into an informal alliance. But this alliance never really went anywhere; one side or the other was always too busy fighting someone else to cooperate in any meaningful way. The Ottomans and Mughals found common cause in war with the Portuguese but the Ottomans were frequently diverting naval assets elsewhere -- to the siege of Malta, to the "White Sea" (Mediterranean) fleet for its inevitable showdown with the Holy League, and so forth. The Ottomans, for some reason, never made defanging the Portuguese a priority.