The calendar used exclusively by the hobbits in J.R.R. Tolkien's The Lord of the Rings. The calendar consisted of twelve months, each with 30 days, and five extra holidays (six on leap years). Each week had seven days, Saturday to Friday; the year always began on a Saturday and ended on a Friday.
The names of the months were Afteryule, Solmath, Rethe, Astron, Thrimidge, Forelithe, Afterlithe, Wedmath, Halimath, Winterfilth, Blotmath, and Foreyule. The holiday of Yule consisted of the day after Foreyule (the last day of the year) and the day before Afteryule (the first day of the year). The Lithe holiday was the day after Forelithe, Midyear's Day, and the day before Afterlithe. In leap years, the additional day of Overlithe was added after Midyear's Day, and was a day of very large and special celebration. Midyear's Day and Overlithe were never given weekday names, though 1 Yule (Friday), 2 Yule (Saturday), 1 Lithe (Friday), and 2 Lithe (Saturday) were.
The Shire year approximately corresponded to our year. 2 Yule, the first day of the year, fell on our modern December 22. When months are discussed in the book, Tolkien generally calls the months by their modern-day equivalents (Afteryule = January, etc) to make it more accessible to the reader.
Bilbo and Frodo Baggins' birthday was given as the 22nd of September. This may correspond directly to 22 Halimath, or if the date is given in our modern calendar, 1 Winterfilth. Similarly, the destruction of Barad-dûr on March 25 may have happened on 25 Rethe, or on 3 Astron.
For more information and a chart, see Appendix D of The Lord of the Rings. Also, the interactive calendar on the Encylopedia of Arda (http://www.glyphweb.com/arda/default.htm) is useful and fun to play with.
This writeup indirectly inspired by a look at my nodeshells.