We have considerable number of journals of some of the important voyages of discovery!

A lot of them were published by the English Hakluyt society founded for exactly the purpose of collecting, translating and publishing original documents relating to discoveries. You can browser their selection here. Because a lot of those works are older, some are now freely available online on sites like gutenberg.org and archive.org.

I am not sure if you were inquiring about any journal, including official ones, or you specifically want journals from some of the other, secondary, crew memebrs. You will have to check each resource to see the exact source of the log.

So here are some examples:

Columbus first voyage log - technically not original log, but 16th century retelling of it by Las Casas, yet considered highly accurate. There are many translation and editions of it online, this is just one

Vasco Da Gama log - log of the journey made by one of the crew members

Magellan voyage - journal from a crew member Antonio Pigafetta

There are many other accounts in the Hakluyt series, some are directly diaries and journals, some a collection of accounts from letters and so.