A Study of Ramucirumab (IMC-1121B) and Paclitaxel in Participants With Solid Tumors

Inclusion Criteria: * Has histologic or cytologic documentation of a malignant solid tumor * Has an advanced solid tumor that is refractory to standard therapy or for which no standard therapy is available * Part A only: Has had 0-1 prior taxane-containing treatment regimens (including taxane monotherapy), which must have been completed at least 6 months before the first dose of study medication (prior bevacizumab is allowed) * Part B only: Prior bevacizumab- and taxane-containing treatment regimens (including taxane monotherapy) are allowed, provided these regimens have been completed at least 6 months before the first dose of study medication * Has resolution to Grade ≤ 1 of all clinically significant toxic effects of prior chemotherapy, surgery, radiotherapy, or hormonal therapy with the exception of peripheral neuropathy, which must not have exceeded Grade 1, by the National Cancer Institute Common Terminology Criteria for Adverse Events, Version 4.0 (NCI-CTCAE v 4.0) * Has an Eastern Cooperative Oncology Group Performance Status (ECOG PS) of 0 - 2 * Has adequate hematologic function. Blood transfusion is allowed but must be completed 48 hours before study drug administration * Has adequate hepatic function (bilirubin ≤ 1.5 times the upper limit of normal \[ULN\], aspartate transaminase \[AST\] and alanine transaminase \[ALT\] ≤ 1.5 x ULN * Has serum creatinine ≤ 1.5 x ULN. If serum creatinine \> 1.5 x ULN, the calculated creatinine clearance (CrCl) should be ≥ 40 milliliter/minute (mL/min) * Urinary protein is \<2+ on dipstick or routine urinalysis (UA) * Must have adequate coagulation function as defined by an international normalized ratio (INR) of ≤ 1.5 and a partial thromboplastin time (PTT) or an activated PTT (aPTT) ≤ 1.5 x ULN * Eligible participants of reproductive potential agree to use adequate method of contraception during the study period and for 12 weeks after the last dose of study medication Exclusion Criteria: * Is receiving concomitant therapy with clinically relevant inhibitors or inducers of cytochrome P450, CYP2C8, CYP3AY and/or isoenzymes * Are currently enrolled in, or discontinued within the last 14 days from, a clinical trial involving an investigational product or non-approved use of a drug or device, or concurrently enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study * Has received a monoclonal antibody within 42 days prior to first dose of study medication * Has received radiotherapy within 14 days prior to first dose of study medication * Has received cytotoxic chemotherapy within 21 days (6 weeks for nitrosoureas or mitomycin C) prior to first dose of study medication * Has a cardiac left ventricular ejection fraction (LVEF) not within institutional limits of normal on a multigated acquisition scan (MUGA) or echocardiogram * Is receiving concurrent treatment with another anticancer therapy, including chemotherapy, immunotherapy, hormonal therapy, radiation therapy, chemoembolization, targeted or other investigational anticancer therapy * Is receiving chronic therapy with nonsteroidal anti-inflammatory agents or other antiplatelet agents. Aspirin use at doses up to 325 milligrams/day (mg/day) and analgesic agents with no or low bleeding risk are permitted * Has a history of uncontrolled hereditary or acquired bleeding or thromboembolic disorders * Has experienced any arterial thromboembolic event, including myocardial infarction (MI), unstable angina stroke or transient ischemic attack (TIA), within 6 months prior to first dose of study medication * Has a history of deep vein thrombosis, pulmonary embolism, or any other significant thromboembolism during the 3 months prior to first dose of study medication * Has experienced a Grade 3 or 4 hemorrhagic event within 3 months prior to first dose of study medication * Has experienced peripheral neuropathy ≥ Grade 2 at any time prior to study entry * Has a bowel obstruction, history or presence of inflammatory enteropathy or extensive intestinal resection, Crohn's disease, ulcerative colitis, or chronic diarrhea * History of gastrointestinal perforation and / or fistulae within 6 months prior to randomization * Has an ongoing or active infection requiring treatment with intravenous antibiotics * Has a serious or nonhealing wound, peptic ulcer, or bone fracture within 28 days prior to first dose of study medication * Has uncontrolled hypertension * Has symptomatic congestive heart failure * Has known brain or leptomeningeal disease * Has known positive status for human immunodeficiency virus (HIV) infection or acquired immunodeficiency syndrome-related illness * Has known active drug or alcohol abuse that would affect participant's ability to comply with study treatment * Has pulmonary lymphangitic involvement that results in pulmonary dysfunction requiring active treatment, including the use of oxygen * Has had major surgery within 28 days prior to first dose of study medication or subcutaneous venous access device implantation within 7 days prior to first dose of study medication * Has an elective or planned major surgery during the course of the trial * If a primary cancer is non-small-cell lung cancer (NSCLC), participant has intratumor cavitation, radiologically documented evidence of major blood vessel invasion or encasement by cancer, or proximity of cancer to major airways * Has received prior ramucirumab (IMC-1121B) therapy * The participant has: * cirrhosis at a level of Child-Pugh B (or worse) * cirrhosis (any degree) and a history of hepatic encephalopathy or ascites resulting from cirrhosis and requiring ongoing treatment with diuretics and/or paracentesis