On request of my friends, I've made this list a public repo.

Internships abroad provide tremendous opportunity to gain invaluable work experience during college.
Please contribute for keeping this resource updated.

DAAD-Wise Scholarship, Germany
MITACS Globalink, Canada.
CalTech SURF Program, USA
CMU Robotics Institute for Summer Scholars, USA
GaTech CRUISE Program, USA
IPAM UCLA, RIPS Program, USA
Princeton ISIP, USA
Brown Summer@ICERM, USA
Space Astronomy Summer Program, Space Telescope Science Institute (STScI), USA
ASU MTBI Summer Program, Arizona, USA
Santa Fe Institute Summer Research Experience, USA
Rockefeller Summer program, USA
Weizmann Institute Visiting Scholarships, Israel
Max Planck Institute for Software Systems, Germany
TU Dresden, Germany
RWTH UROP International, RWTH Aachen
CERN Summer Student Program, Switzerland
CERN OpenLab for Computer Science Undergraduates, Switzerland
Summer Fellowship at ETH Zurich, ETH Zurich, Switzerland
Summer at EPFL, Lausanne, Switzerland
ISternship Summer Student Program, IST Austria
UNSW Civil and Environmental Engineering Research Internship, Australia
SPIKE @ UNIST, South Korea
TIGP-IIP, Sinica, Taiwan
NTHU Summer Internship Program, Taiwan
IVISP, HKUST, Hong Kong
SURP, CUHK, Hong Kong
OIST Research Internship Program, Okinawa, Japan
Auckland Summer Research, New Zealand

S.N. Bose Scholarship (IUSSTF), USA
USC Viterbi India Program, USA
IUSSTF Khorana Program for Scholars, USA
Shastri Research Student Fellowship, Canada (Now, integrated with MITACS)
NTU-India Connect, NTU, Singapore
Charpak Global Scholarship, France
Indian Student Internship Program at NTHU, Taiwan
LIGO IndiGo, CalTech, USA

Summer Research Fellowship Programme, IAS-INSA-INS (Tri-Academy of Sciences) for IISc/IIT/CSIR/ISRO etc.
IITB Research Internship Award, IIT Bombay
IITK SURGE Program, IIT Kanpur
CMI Internship, Chennai Mathematical Institute