How many newspapers are there in this world? Many. What newspapers do university libraries subscribe to? Many. Which newspapers are free? No idea.
Adelaide University Library - newspapers listing
Straits Times Suspended 14 February 1942 issue; resumed 7 September 1945 issue
British Library - full-text, word-searchable, newspapers listing; many not available for online reading outside the British Library reading room in London
Nineteenth Century Serials Edition (NCSE)
Digitised newspapers in Singapore