Unlike corporations, partnerships and sole proprietorships do not provide limited personal liability for business debts. This means that creditors of those businesses can go after the owners' personal assets to collect what's due. However, organizing and operating a partnership or sole proprietorship is much easier than forming a corporation, because no formal paperwork is required.
A limited liability company (LLC), on the other hand, does offer limited personal liability, like a corporation. And while formal paperwork is required to form an LLC, running an LLC is less complicated than running a corporation. LLC owners do not have to hold regular ownership and management meetings or follow other corporate formalities, for example.
Corporations also differ from other business structures in the way they are taxed. The corporation itself must pay corporate income taxes on its profits -- whatever is left over after paying salaries, bonuses, and other deductible expenses. In contrast, partnerships, sole proprietorships, and LLCs are not taxed on business profits; instead, the profits "pass through" the business to the owners, who report business income or losses on their personal tax returns.
Finally, for guidance on deciding which ownership structure is most suitable for your business, read Nolo's article Choosing the Best Ownership Structure for Your Business.