"Phaedo" is one of Plato's best and most important works. Though well worth reading by itself, the fact that it is widely anthologized - e.g., in The Trial and Death of Socrates - makes it very hard to justify a standalone.
Though apparently early and not as complex or philosophically influential as later ones, "Phaedo" is immensely important in portraying Socrates' death. Along with the aforementioned dialogues, it is our clearest picture of the historical Socrates and would be invaluable for this alone. Indeed, I have read hundreds - perhaps thousands - of books, and this is one of my ten or so favorites, mostly because of how moving the depiction of the great man's last days is. The story of Socrates' last moments is part of world literature's very fabric, an immortal part of Western cultural heritage. However, the works have great value even aside from this; a few have indeed questioned their historical veracity. This does not affect their philosophical, literary, and political worth, which is of the highest, making the book doubly essential.
"Phaedo" ostensibly details Socrates' last moments, including his last look at his wife and child, his last dialogue, his last words to friends, and his actual death. A large part of Socrates' image comes from this, and its potential historical value is inconceivable, though its historicity can easily be doubted since the work itself strongly suggests that Plato was not there. Even so, it is likely accurate in regard to the things that really matter and certainly a fine account of how it very well could have been. It is extremely moving; shot through with pathos, it is one of the most affecting things I have ever read. One can surely not read it without being overcome by emotion; I can hardly even think of it without misty eyes. Anyone who respects and admires this central Western civilization figure will be profoundly touched; his famous last words seem comic out of context but are very much otherwise here, telling us much about Socrates and moving us yet further. This would be one of the greatest works of all-time if it had no other aspect, but it is also a fine dialogue appropriately dealing mostly with death. Plato examines perennial questions like the soul's immortality and metempsychosis very thoroughly and thought-provokingly, and the conclusion - unsurprisingly, given the circumstances - has uncharacteristic certainty. It may not convince our cynical, empiricist, science-loving, twentieth century-surviving age, but the argument is certainly well-made and in many ways admirable. The dialogue touches on other important subjects also and is generally seen as the culmination of Plato's early, Socrates-centered thought.
The ever-important translation issue must also be kept in mind. It goes without saying that anyone who cares about intellectual issues, especially applied ones, must know Plato, as should anyone who wants to be even basically well-read. However, this is far easier said than done for most; he is so different from what now passes for literature, to say nothing of pop culture, that he is virtually inaccessible to general readers. Yet the importance of persevering cannot be overemphasized; the payoff is well worth the effort. As nearly always in such cases, reading him becomes far easier after the initial difficulty; no attentive reader will ever think Plato easy reading, but he is utterly absorbing once we get used to his style. He has a near-poetic beauty that all agree has never even been remotely approached in philosophy, and such mesmerizing prose is rare in any genre. His dialogues are an incredible form at once intellectually and aesthetically pleasing - an inspired combination that has perhaps never been bettered; many have appropriated it, but none have matched it. All this means that picking the right translation is probably more important with Plato than any other writer. For the average reader, the more recent, the better is generally true, though older translations like W. H. D. Rouse's and Benjamin Jowett's are still very accessible. The important thing is to read Plato in some form, and those who happen on a translation that does not work for them should keep trying until their mind opens in a truly new way - and once done, it will never close again.