I can say Thomas Crocker was an immigrant only because I know he died here and was born in England. He is often said to have been born in 1633 and to have been the son of Hugh Crocker and Elizabeth Colleton, and to have been christened at St Olave, Exeter, Devonshire, England. Some of those facts may be true, none of them may be true, or all of them may be true, but many family historians are leaving his parentage blank. So we will simply say he was born in England.
It seems that he was in New London, Connecticut by 1667, when he married Rachel Chappell, daughter of George Chappell and Christian possibly Bell Chappell. I've not found speculation as to when he emigrated to America, or why. If indeed he was the son of Hugh and Elizabeth, he may have come at a young age with his brothers, or followed soon after. Perhaps his parents had the foresight to send him out of the country before the Civil War broke out. Hugh, mayor of Exeter, if this is the correct Hugh) was a Royalist but his sons seem to have tried not to take sides in America. Or it may be that he didn't come until later. He seems to have bought a house in New Street in New London, Connecticut in 1660, although other sources say he didn't arrive until a few years later, and was named in a land grant of 1663 and again in 1704.
He and Rachel had at least eight children, born between 1669 and 1685 (none named Hugh!). We don't know what he did for a living but perhaps he worked in the maritime trades. His father in law was a carpenter, so perhaps he learned that, or a similar, trade. I've not yet located a will for him, which could probably tell us a good deal more than we know now. Thomas Crocker died January 18, 1715/16 and it appears that Rachel lived until 1728. Once Thomas arrived in New London, that is where he stayed (unless he made trips for trade purposes, for which there is no indication).
Thomas may or may not have left other records, showing land or court records, church affiliation, and town offices or responsibilities. So far, I haven't found them. He is pretty much a mystery, but he is one of the men who, however low their social status may (or may not) have been, made America.
The line of descent is
Thomas Crocker-Rachel Chappell
John Crocker-Mercy Tubbs
Rachel Crocker-Kingsland Comstock
Rachel Comstock-John Eames
John Eames-Elizabeth Longbottom
Harriet Eames-James Lamphire the missing
Susan Lamphire-Joseph B Eddy
Susan Eddy-Hiram Stanard
Louis Stanard-Mary Alice Hetrick
Etta Stanard-Loren Holbrook
Gladys Holbrook-Richard Allen