1. Greatest: I'd give it to DiMaggio, with Hershiser second.

2. Underrated: That time the A's won 20 straight games to surge to the division title- not the actual record (26 with a tie in 1916 for the NY Giants), but team win streaks are more impressive to me than player streaks, and I remember the A's streak.

I think the greatest streak is DiMaggio's 56 gamer.  I read somewhere that statistically speaking, the odds against a player hitting in that many consecutive games is truly mind boggling.  The analysis indicated that it is unlikely to be broken for an extremely long time, unless the game undergoes some kind of fundamental change favouring hitters.  Might have been Bill James who did that analysis, I'm not sure.

For something off the radar a bit, there are dozens.  For a recent one, how about Mark Buehrle's record set in 2009 when he retired 45 batters in a row.  Got the last batter out in one appearance, pitched a perfect game next appearance, then retired 17 in a row to start his next game after the perfecto.  As a Giants' fan I remember the old record of 41 in a row set by a pitcher named Jim Barr, who did it by retiring 21 in a row to end a game, then 20 in a row to start his next game.  Barr's record was set in 1972 and tied by Bobby Jenks in 2007 over the course of a large number of games.

If you can call 2 of something a streak, then Vander Meer's consecutive no-hitters is right up there, and for most unusual, Dave Stieb's consecutive games with a no-hitter broken up with 2 outs in the 9th inning and 2 strikes on the batter, both times on rather flukey hits.

Some others that you don't hear about very often - consecutive stolen bases without being caught, 50 by Vince Coleman; consecutive plate appearances with a hit, 12 by Walt Dropo and Johnny Kling; consecutive games without striking out, 115 by Joe Sewell; consecutive shutouts, 6 by Don Drysdale; consecutive saves converted, 84 by Eric Gagne; consecutive batters struck out, 10 by Tom Seaver and Eric Gagne; consecutive seasons played with 1 team, 23 by Brooks Robinson and Carl Yastrzemski; and consecutive all-star game appearances, 24 by Willie Mays and Stan Musial

Mags, I agree with you, but minor factual correction --it's actually two since Cobb 100 years ago. Sisler (41) in '22 and Rose (44) in '78.

In the last 25 years, only two players (Molitor with 39 in 1987 and Rollins with 38 over 2005-06) has even cleared 35. Within one season, only Utley (35 in '06), Luis Castillo (35 in '02) were the only ones to even reach 35.

As I recall, it was the fella Jay players call "Skip" these days.

I was in Ohio at the time and remember seeing Farrell as obviously ready to develop into a multiple-time 20-game winner ...

I hate to get too analytical about something like this question, but...It is important to understand the way the game has changed over the years.  Strikeout rates have gone way up over the last 50 years, which has led to declining batting averages.  There is the odd player who bucks the trend (Carew, Brett, Gwynn, Ichiro), but the general decline makes it much, much less likely that a player will put together a long hitting streak than it was in the time of Sisler, Hornsby, Gehrig,  and DiMaggio (i.e the pre-WWII lively ball era).

I have to disagree with the strikeouts lead to lower average idea - strikeouts have been rising in baseball pretty steadily for a long time, with only a massive increase in the early 1960s departing from the trend all that much (after the adjustments to the game, strikeouts basically fell back to the long term trend line). Since 1980, strikeouts have gone from about 5 a game to 7 per game (for each team), but BA has held pretty stready. To me, this implies that hitters have been making a relatively successful tradeoff between less contact and harder contact. I'm curious where the Strikeout trend will end - there has to be an upper limit, but since starting below 3/game at the beginning of the live ball, it's been heading up ever since. Strikeouts still lower the chances of a long hit streak without lowering BA, I think, because of the increase in balls in play (noisier data leads to longer tailed outcomes), but not the AVG itself.

I find it surprising that BB rate has been virtually unchanged over the decades - hitters may be trying for more walks, but pitchers seem to normalize their strategies to where they come out to between 3 and 3.5/game.  

There was an indisputable rise in BAs in the pre-war era, where MLB hit .275-.295, which would make streaks more likely, though. DiMaggio still had by far the longest stretch in that era, of course.

The one guy who "should" have had a long hit streak in the last decade is Ichiro - doesn't walk much, bats leadoff, hits for a high average, team is often behind in the ninth inning at home (lately anyway), never leaves a game for defensive reasons or is pinch-run for. I think his best is 27, which may actually be below what is expected of his career. But Ichiro's 200+ hits/season streak is very impressive - 10 now, and he could add several more seasons to it.