Vorinostat (MK-0683, SAHA [Suberoylanilide Hydroxamic Acid]) + Lenalidomide + Dexamethasone in Multiple Myeloma (MM) (MK-0683-074)

Inclusion Criteria: * Is a male or female at least 18 years old * Has relapsed or refractory MM and has had at least one prior therapy * Female participants of childbearing potential must have 2 negative serum pregnancy tests prior to receiving the first dose of study drugs * Female participants who can become pregnant must agree to use 2 separate forms of effective birth control at the same time, 4 weeks before, while taking, and for 4 weeks after stopping lenalidomide; post menopausal participants should be free from menses for \>2 years, or are surgically sterilized * Male participant agrees to use an adequate method of contraception for the duration of the study, even if the participant has undergone a successful vasectomy * Male participants must agree to use a latex condom during sexual contact with a pregnant female or a female who can become pregnant; this is required for the duration of the study, and for 4 weeks after stopping therapy * Has at least 3 weeks washout prior to treatment * Is able to swallow capsules and is able to take or tolerate oral medications on a continuous basis Exclusion Criteria: * Has prior treatment with a histone deacetylase (HDAC) inhibitor * Has prior allogenetic bone marrow transplant * Has received intravenous antibiotics, antiviral, or antifungal agents within 2 weeks prior to the start of the study drug * Uses illicit drugs, substance abuse or had a recent history (within the last year) of drug or alcohol abuse * Is pregnant or breast feeding or expecting to have a baby during the course of the study * Has human immunodeficiency virus (HIV) infection * Has Hepatitis B/C infection * Is currently receiving treatment for another type of cancer other than skin or cervical cancer that has not been in remission for 5 years or longer