The Haywards and many others joined the Church of Jesus Christ of Latter-day Saints in Europe and traveled across the ocean to join the Saints in Utah.
The BYU Harold B. Lee Library has an interesting new site called Mormon Migration with information from many ship records. It has tens of thousands of emigrant records, so if your ancestor crossed the ocean with the Latter-day Saints, you have a good chance of finding the ancestor in this database.
Here are links to various ancestors of mine and the information about their voyages across the ocean. After following the link, make sure you click "Accounts for this voyage" to read journal and autobiography entries from passengers on the crossing.
I am only including the head of household in this list.
Gammon Hayward (1853, International)
Philip Pugsley (1853, Falcon)
John Sutton (1853, Elvira Owen)
Samuel Bryant (1854, Julia Ann; from Australia)
Thomas Parkinson (1854, Julia Ann; from Australia)
George Jarvis (1857, George Washington)
Ann Harris Hamilton McQueen
Elizabeth Cripps (1861, Underwriter)
James Glade (1861, Monarch of the Sea)
David Thomas (1862, John J. Boyd)
Jens Oveson (1863, B.S.Kimball)
Charles Cripps (1863, Amazon)
Ove Oveson (1864, Monarch of the Sea; includes his account of the trip)
Jens Christensen (1866, Kenilworth)
Christiane Christensen (1866, Kenilworth)
Richard Litson (1866, John Bright)
Mary Marsden (1866, St. Mark)
Archibald Hill (1867, Manhattan; he was a returning missionary, not an immigrant, and he was in charge of the company of immigrants)
Mary Ann DeFriez (1877, Wyoming)
James Hamilton (1884, Arizona)
Lucy Green (1888, Wisconsin)
Thanks to Keepapitchinin for the link to Mormon Migration. For an article with information about the Perpetual Emigrating Fund of the Church of Jesus Christ of Latter-day Saints, including links to many sources about the fund and about Mormon migration, see the article, "The Perpetual Emigrating Fund."
The ocean picture is from www.flickr.com/photos/brian-m/314646922/, used under a Creative Commons license.