Troilus and Cressida is one of Shakespeare's more difficult—and, some might say, unpleasant—plays to read or to watch. Derived (and diverging) from classical and medieval accounts of the siege of Troy—notably Homer's Iliad and Chaucer's fourteenth-century Troilus and Criseyde—the play offers a debased view of human nature in war-time and a stage peopled by generally unsympathetic characters. Like many of the great tragedies, the broad theme is the relationship of, and conflict between, personal life and the interests of the state—in this case, the conflict between the romance of the title characters and the war-time politics that send Cressida away from her lover into the Greek camp. But this theme coexists with a general pessimism unmatched even in the darkest tragedies, as classical heroes like Achilles and Ajax are presented as self-absorbed thugs, and the central romance of Troilus and Cressida is rhetorically reduced to lust, so that in the memorable phrase of the Greek slave Thersites, "all the argument is a whore and a cuckold" (II.iii.75).
Structurally, the play presents difficulties as well. There is an uneasy division between the romance and the political action; the two plot lines are not fully integrated until the later stages of the play, giving the action a disjointed feel. At the same time, Shakespeare uses anti-climax throughout the play, so that scenes that we think will be critical turn out to be letdowns. This is especially true in the duel between Hector and Ajax in Act IV, which ends in a draw, and again in Act V's final battle, in which the events we expect do not transpire: Troilus is not avenged for the loss of his beloved, and Hector does not have a climactic duel with his great adversary, Achilles, who instead ambushes him unarmed and kills him. The events of the play, then, are almost defiantly unsatisfying.
There are many redeeming qualities to Troilus and Cressida, however, including some of the finest philosophical speeches in all of Shakespeare—which, some critics have suggested, are more impressive outside the context of the play than within it. The argument between Hector and Troilus over the value of fighting to keep Helen in Troy is notable for its rhetoric and depth of insight, and so too are the speeches of Ulysses, one of the play's most interesting and intelligent characters, who discourses at length on the role of order in society (as displayed in the Greek camp) and on the relationship between time and reputation. Thersites, too, is an interesting and entertaining character—while his language tends to be abusive and coarse, he is the play's only moralist, and often seems to speak for the playwright as he provides bitter, scolding commentary on the crimes and lusts of his supposedly more heroic fellow characters.
I just finished reading Troilus and Cressida in my effort to read all Shakespeare by his 450th birthday. It wasn't a favorite play, and I probably could have had a very happy life without ever reading it. But in case you're interested, here's my take: