Of all the famous Dutch masters during the Late Renaissance and Early Baroque periods, none surpass Rembrandt van Rijn in either historical importance or artistic merit. His aesthetic has been much-imitated, a testament to the inspirational grip they exert on their viewer. Key aspects of his style are instantly recognizable to even the casual fine art enthusiast: his penchant for chiaroscuro lighting amidst dark backgrounds; the feverish intensity of his subjects, who are often shown seemingly in action rather than composed; and the recurring use of Biblical and historical subject matter, not to mention an even more prolific output of portraits commissioned (including works commissioned by the Court of the Hague).
The more educated viewer might also be aware of Rembrandt's remarkably thick handling of paint, which often seems to protrude from the canvas rather than invite a recession into space (in the Renaissance tradition.) However one recognizes a Rembrandt, however, the strength of his talents is such that encounters with his work leave an indelible imprint.
That said, Rembrandt's fame derives not only from the hundreds of paintings he completed (his output is believed to total as many as several hundred works); Rembrandt is also remembered for his profligate spending habits, which famously resulted in him filing for bankruptcy in 1656. If "baroque" connotes excess, it is most appropriate that Rembrandt stands as the most famous painter of the Baroque age, as he lived well beyond his means.