Large Language Models (LLMs) are increasingly integrated into consumer and enterprise applications. Despite their capabilities, they remain susceptible to adversarial attacks such as prompt injection and jailbreaks that override alignment safeguards. This paper provides a systematic investigation of jailbreak strategies against various state-of-the-art LLMs. We categorize over 1,400 adversarial prompts, analyze their success against GPT-4, Claude 2, Mistral 7B, and Vicuna, and examine their generalizability and construction logic. We further propose layered mitigation strategies and recommend a hybrid red-teaming and sandboxing approach for robust LLM security.