Does the Bible suggest that the earth is round? I've heard the term "flat earthers" mentioned in regards to Christians. Does the Bible suggest that the earth is flat or that the earth is round?

What scripture is there that suggest a round earth or flat earth?
In addition to Isaiah 40:22, which Ashansky pointed out, there's also Job 26: 7, which states that the earth is hung "upon nothing".  This is quite a difference from, for example, the Greek idea of Earth supported upon Atlas's shoulders, or the Hindu notion of Earth resting upon the back of an elephant which stands on the back of a turtle which swims in a vast ocean.

Also, Luke 17:31-36 speaks of people being taken away into heaven at (or before, but that's a matter for a different question) the time of the Second Coming, and states that some will be taken at night, and some in the daytime, even though it's supposed to happen all at once.  That's not possible on a flat earth model.

The idea of a flat earth is not found in the Bible or in ancient Christian thought.  The notion that people thought it was was invented almost simultaneously, but apparently independently, by two 19th-century authors. One came up with the idea for dramatic purposes; the other did so quite maliciously for the specific purpose of slandering and discrediting Christianity:


  No one before the 1830s believed that medieval people thought that the earth was flat.
  
  The idea was established, almost contemporaneously, by a Frenchman and an American, between whom I have not been able to establish a connection, though they were both in Paris at the same time. One was Antoine-Jean Letronne (1787-1848), an academic of strong antireligious prejudices who had studied both geography and patristics and who cleverly drew upon both to misrepresent the church fathers and their medieval successors as believing in a flat earth, in his On the Cosmographical Ideas of the Church Fathers (1834). The American was no other than our beloved storyteller Washington Irving (1783-1859), who loved to write historical fiction under the guise of history. His misrepresentations of the history of early New York City and of the life of Washington were topped by his history of Christopher Columbus (1828). It was he who invented the indelible picture of the young Columbus, a "simple mariner," appearing before a dark crowd of benighted inquisitors and hooded theologians at a council of Salamanca, all of whom believed, according to Irving, that the earth was flat like a plate. Well, yes, there was a meeting at Salamanca in 1491, but Irving's version of it, to quote a distinguished modern historian of Columbus, was "pure moonshine. Washington Irving, scenting his opportunity for a picturesque and moving scene," created a fictitious account of this "nonexistent university council" and "let his imagination go completely...the whole story is misleading and mischievous nonsense."
  
  -- Jeffrey Burton Russell, The Myth of the Flat Earth


Also, from an extrabliblical source, it seems that Clement, bishop of Rome from the early Christian period, had correct knowledge of the earth.  He spoke of antichthones (Greek, literally "people on the other side of the world") and stated that:


  The ocean is impassable to men; and those are worlds which are on the other side of it, which are governed by these same arrangements of the ruling God.
  
  -- cited here with the rather indecipherable "Clemens Rom., Ep. i., ad Cor., c. 20."