At the root of most comments so far, correctly, is their role in deterrence. ICBMs provide a very fast, mainline strike option. Missile submarines provide a more secure second strike. Strategic bombers provide a very visible but reversible escalation step: you can launch the bombers to show you're serious and hope for one last-minute round of crisis negotiations, whereas launching missiles will prompt an immediate counterattack, and surfacing your missile submarines would just compromise their location without accomplishing anything politically. It's not so much that you're ordering a nuclear attack and then changing your mind so much as ordering them to go forward and hoping to give the enemy one last chance to blink and stand down.
Second, I don't think we should neglect the bureaucratic rationale for them, either. From the perspective of at least some of the professionals involved, the fact that we have invested thousands of careers and billions of dollars over many years in maintaining a strategic bomber force is reason enough to keep the bomber force around, even if it is the least useful leg of the triad.
Third, you can use the strategic bombers for conventional operations, so even if their central mission is obsolete, they're not exactly useless.