There are a number of resources on campus that helps organizations (whether a startup, a corporation, a non profit, an academic institution, a government agency, or the United Nations) place undergraduate students in internships or externships.
Cross departmental project based research program that is backed by companies like General Motors. Reaches 120+ sophomores and juniors. Year round.
A year long professional development program for sophomores
The MIT International Science and Technology Initiative (MISTI) matches international employers with undergraduate students for an overseas internship experience. MISTI has offerings in 25+ locations.
This program pairs freshmen, sophomores and juniors with MIT deltav alumni startups. MIT deltav is run by the Martin Trust Center and is a capstone summer accelerator program for student startups who are ready to build a successful business at scale when they graduate from MIT.
MIT Externships pair students with alumni during IAP so students can experience these companies for a short time. They can lead to summer internships and full time positions.