Other Shi'a, including the Ismailis, believe that the last Imam died, and that modern-day Shi'a must instead live by the canonical Imams' precepts. Another possible solution, held by no-one I know of, is that the Imam's line has lasted to this day - but that the rightful heir to 'Ali is a mystery.
Actually, David is mistaken, the Ismailis do indeed believe that the line of Imams has continued unbroken. It is an article of faith that the line can never be broken. The Aga Khanis (or Nizaris) believe in fact that the Aga Khan is that living Imam, descendant of Ali AS. The Bohras, my community, believe that the 21st Imam went into occlusion and continued his line. At the time of occlusion, at the close of the Fatimid dynasty, religious authority was transferred to the office of Dai ul-Mutlaq of which there have been 52 officeholders since, the current Dai being Syedna Mohammed Burhanuddin (TUS). It is an article of faith that the hidden Imam - a blood line descendant of the 21st Imam - remains the embodiment of spiritual authority but the Dai excercises that authority on his behalf.
Again, I refer any interested readers to the book Mullahs on the Mainframe (review) for more information on the Bohra community, the office of the Dai ul Mutlaq, and the beliefs of the Fatimi Ismaili Shi'a.