St. Jude letters are a type of chain letter, promising good luck for those who forward it, and bad luck for those who do not. While St. Jude is not a strict category of chain letters, they originally were religious in nature, and included specific references to St. Jude (the Patron Saint of lost causes). The format of the original St. Jude letters has been used extensively, often with all religious references removed; this non-religious format of the letter may or may not be considered a St. Jude, depending on the speaker.
St. Jude letters are not pyramid schemes, as they do not ask for money. While the earliest ones asked for each letter to include five cents, which was to be donated to a church, this probably is not enough to qualify it as a pyramid scheme (unless it was started by the Church...) Here is a patchwork St. Jude letter, in which I try to include all of the standard aspects that characterize St. Jude letters.
Before anything else, I would like to tell you that St. Jude Thaddaeus will help you in everything you encounter.
Nothing in part will end to this chain so give it to a devotee of St. Jude Thaddaeus by mail. In thirteen days, you will receive a surprise, no matter how impossible.
The president of Brazil received this letter but did not give importance to it. In thirteen days his son died.
Senator Sola received it and sent it within 13 days; he won a lottery.
Exequel Arellano made 24 copies, sent it within nine days and received a million dollars.
Antonio Martines received it and forgot to send copies before 13 days. He told his secretary to type it up, but forgot to send them. He lost his job.
Isabel Buena lost her copy and lost her life. Do not forget to send copies before 13 days. For the favor of the Virgin Mary of Mt. Carmel, pray one Our Father, three Glory Be. This has been sent to us. It is not a game and you will receive luck. Within 13 days, send a copy to your friends who need it most.
St. Jude
You will note that this is focused on South America and South Americans; the St. Jude letter apparently started in SA in the early 1980s, and were written in Spanish. This example is pieced together from letters found in the Paper Chain Letter Archive*. As you can see, some of the most common aspects of 'Good Luck' chain letters seen today arose in St. Jude letters.
In the early 1990s a new St. Jude fad was spawned; the St. Jude classified ad. These can be a simple prayer or thanks to St. Jude:
Thank you Sacred Heart of Jesus and St. Jude for prayers answered. --EMK
But the interesting ones take a form very close to that of a chain letter; the example below also comes from Paper Chain Letter Archive**.
SAINT JUDE NOVENA. May the Sacred Heart of Jesus be adored, glorified, loved and preserved throughout the world now and forever. Sacred Heart of Jesus, pray for us. St. Jude, Worker of Miracles, pray for us. St. Jude, Helper of the Hopeless, pray for us. Say this prayer 9x a day for 9 days, then publish and your prayers will be answered. It has never been known to fail. R.P.
This is the standard 'Good Luck' novena, although "Thank You, St. Jude" is often appended to the end, and there may be other conditions, such as "You must not pray for personal, material gain". I very much doubt that any major branch of the Christianity would consider this an acceptable devotion, but it was very popular for a while there. A closely related prayer, also with miraculous results guaranteed, uses the Blessed Virgin Mary as its focus. It too requires publication of some sort before the prayer will come true.
In a truly bizarre twist, this novena will sometimes promise to grant your wish even if you don't believe. I assume that this is a holdover from the chain letter; it certainly doesn't seem to belong in a prayer.
* Paper Chain Letter Archive:
http://www.silcom.com/~barnowl/chain-letter/archive/!information.htm
Specific examples used,
http://www.silcom.com/~barnowl/chain-letter/archive/le1984-05_mx_tagalog_q24.htm (1984)
and
http://www.silcom.com/~barnowl/chain-letter/archive/le1995-09_mex_s5c_q24.htm (1995)
You can find a standard 'globalized' version at:
http://www.silcom.com/~barnowl/chain-letter/archive/le1994-11_dl_wlcj.htm
** http://www.silcom.com/~barnowl/chain-letter/evolution.html
http://www.geocities.com/Heartland/4251/stjude.html contains a slightly longer version. I find it interesting to note that many versions of this prayer, including the one at this site, promise results by the eighth day, although they require that you pray for nine.