Was she? O'Conner and Robertson (1) state the following:

[Lovelace] produced an annotated translation of Menabrea's Notions sur la machine analytique de Charles Babbage (1842). Babbage (2) describes how this came about:-

[...] We [Lovelace and Babbage] discussed together the various illustrations that might be introduced: I suggested several, but the selection was entirely her own. So also was the algebraic working out of the different problems, except, indeed, that relating to the numbers of Bernoulli, which I had offered to do to save Lady Lovelace the trouble. This she sent back to me for an amendment, having detected a grave mistake which I had made in the process.

The notes of the Countess of Lovelace extend to about three times the length of the original memoir. Their author has entered fully into almost all the very difficult and abstract questions connected with the subject. [...]

In the annotations, which were called "Notes", Ada Lovelace described how the Analytical Engine could be programmed and gave what many consider to be the first ever computer program. [italics added]

Or wasn't she? On the other hand, Bromley (2) says

Ada Lovelace has sometimes been acclaimed as the 'world's first programmer' on the strength of her authorship of the notes to the Menabrea paper. This romantically appealing image is without foundation. [italics added] All but one of the programs cited in her notes had been prepared by Babbage from three to seven years earlier. The exception was prepared by Babbage for her, although she did detect a 'bug' in it. Not only is there no evidence that Ada Lovelace ever prepared a program for the Analytical Engine but her correspondence with Babbage shows that she did not have the knowledge to do so."
 

Notes

Selected Works of Ada Lovelace

Luigi F. Menabrea, "Sketch of the Analytical Engine Invented by Charles Babbage, Esq.," with notes by trans. Ada Lovelace (Richard and John E. Taylor, 1843). Also available online at http://www.fourmilab.ch/babbage/sketch.html (Fourmilab, Switzerland, accessed 2004 Sep 19).

Betty Alexandra Toole, "A Selection and Adaptation From Ada's Notes found in 'Ada, The Enchantress of Numbers,' by Betty Alexandra Toole Ed.D. (Strawberry Press, Mill Valley, CA)," http://www.agnesscott.edu/lriddle/women/ada-love.htm (Agnes Scott College, accessed 2004 Sep 19). From Sanket Dalal, Chad Wagonner, 2004 Sep 9.

1. John J. O'Conner and Edmund F. Robertson, "Ada Lovelace," http://turnbull.dcs.st-and.ac.uk/history/Mathematicians/Aiken.html (School of Mathematics and Statistics, University of St. Andrews, Scotland, accessed 2003 Sep 13).

2. Allan G. Bromley, "Difference and Analytical Engines," Chap. 2 in Computing Before Computers (Ames, IA: Iowa State University Press, 1990). Also available online at http://www.computerhistory.org/collections/DocumentArchive/Documents/Books/Computing Before Computers/CBC-Ch-02.pdf (Computer History Museum, accessed 2003 Mar 19).

Bibliography

Betty Alexandra Toole, Ada, the Enchantress of Numbers: Prophet of the Computer Age, paperback (Critical Connection, 1998).

Betty Alexandra Toole, Ada, the Enchantress of Numbers: A Selection from the Letters of Lord Byron's Daughter and Her Description of the First Computer (Critical Connection, 1998).

Benjamin Woolley, The Bride of Science: Romance, Reason, and Byron's Daughter (McGraw, 2002).