We're going to focus predominantly on the guys who pitched in the past half-century. However, there are a few worth mentioning who were unable to hurl a no-hitter even before the mound was lowered in 1969.

Grover "Old Pete" Alexander (1911-1930)
FanGraphs No. 9; Baseball Reference No. 5

Proof of how difficult/random it is to throw a no-hitter, Alexander ranks second in MLB history with 90 complete-game shutouts in his career, yet he never managed to do one hitless.

There were plenty of close calls, of course. In his rookie season alone, he threw a one-hit shutout in a win against Cy Young and had a relief appearance in which he threw eight innings without allowing a hit. Four years later, Alexander had not one, not two, not three, but four one-hit shutouts in a single season. So close, but no cigar.

Kid Nichols (1890-1906)
FanGraphs No. 19; Baseball Reference No. 4

Nichols wasn't quite the shutout artist that Alexander was, but 48 in a career is nothing to sneeze at. Neither Baseball Reference nor FanGraphs offers game-by-game logs prior to 1901, but even in the latter stages of his career, Nichols tossed a 1904 two-hitter in which one of the hits was an eighth-inning home run.

Tim Keefe (1880-1893)
FanGraphs No. 29; Baseball Reference No. 15

As just noted, we don't have game logs for Keefe, because his entire career took place prior to 1901. The record books do say he pitched 554 complete games and 39 shutouts, though, and there were six seasons in which he led the league in hits allowed per nine innings pitched. Safe to assume he flirted with a no-no or five along the way, but he never got one.

Lefty Grove (1925-1941)
FanGraphs No. 13; Baseball Reference No. 6

Grove led the league in ERA nine times in his career, led the league in strikeouts in each of his first seven seasons, pitched 35 complete-game shutouts and was named the 1931 AL MVP with 31 wins.

But it wasn't until his next-to-last season that he finally flirted with a no-hitter. In the 1940 season opener against the Washington Senators, Grove carried a perfect game into the eighth inning before an error and back-to-back singles ruined his quest for history.

Robin Roberts (1948-1966)
FanGraphs No. 26; Baseball Reference No. 22

Starting with the 1950 Phillies—AKA the Whiz Kids—Roberts had a dominant seven-year run, earning NL MVP votes in each of those seasons. He racked up 45 complete-game shutouts in his Hall of Fame career. And even though he allowed the second-most home runs (505) in MLB history, he did have a pair of one-hit shutouts, plus one start in May 1954 in which he allowed a leadoff home run to Bobby Adams before retiring the next 27 batters.