Some of the major international rankings, all freely available:
Academic Ranking of World Universities (ARWU)
Published by ShanghaiRanking Consultancy, using Web of Science data plus other factors e.g. winners of Nobel Prize and Fields Medals. More than 1200 universities are ranked each year, the best 500 are published.
CWS Leiden Ranking
Produced by Leiden University, using Web of Science data. Includes over 800 universities worldwide.
QS World University Rankings
More than 900 universities from over 80 countries are ranked, by assessing university performance across four areas: research, teaching, employability and internationalisation. Based on 'hard data', data from Scopus and from surveys.
THE World University Rankings
Produced by the THE (Times Higher Education), using Scopus and survey data. Judges research-intensive universities across "their core missions: teaching, research, knowledge transfer and international outlook."