Are there any examples of individual Space Marines who deserted their Chapter in favor of living for themselves?
While not all Renegade Astartes chapters turn directly to Chaos (or so they think), many end up being swayed after turning away from the Imperium. But if you're strictly talking about individual Marines (or small groups) rather than whole Chapters, you're thinking of Blackshields.
The exact origins of the Blackshields phenomenon remains a mystery. However, what is known is that many types of Blackshields existed, most defined by the circumstances of their formation. Some were Astartes driven beyond their limits, consumed by the grief and insanity of the Heresy. Some were so broken in mind and spirit they no longer recognized or acknowledged any lord, becoming determined to forge their own path in the Galaxy. Others were mere raiders determined to claiming their own domains from both sides. Some thought they were still continuing the work of the Great Crusade while others established petty empires, enslaving those they came across. Perhaps the most mythic type of Blackshields were those who actively turned on their own Primarch and Legion.
Blackshields are Marines who, for one reason or another, have left their patron Chapter to forge their own way. Typically, they renounce their Chapter's colours and heraldry, painting their armour plain black - hence the name. The reasoning for their departure is varied - some are the last remaining survivors of a decimated Chapter, while others have been exiled for some transgression against their Chapter's doctrines. Oftentimes, these Blackshields forge a new destiny for themselves by undertaking suicidal crusades against the Imperium's enemies, or by joining the Deathwatch (See: Deathwatch Black Shield). Others simply go renegade, and become pirate lords or mercenaries.
Similar to Blackshields are the Knights-Errant, who were Astartes individuals or groups who found themselves on the wrong side of the Horus Heresy, such as Nathaniel Garro, a former Death Guard who remained loyal to the Imperium when his Legion rebelled.