The classical muhaddithoona such as Imam Bukhari, Muslim and Imam Malik and many others, compiled thousands of ahadith into their collections and gave it stringent conditions to verify the validity of each this is also known as the categories of hadith.
Previoulsy these were only available in physical book formats, with the emergence and demand for electronic formats such as pdfs and websites. Muslims have created such and have made it publicly and easily accesible for all.
There are many websites which list the hadith collections, from experience I know that some of the English translations available online contain grammatical errors and aren’t easily readable.
I am going to list my favourite websites (some incomplete) which have good translations and search facilities.
This is my favourite website for ahadith collection online it has 12 collections all listed (some incomplete). As well as listing the translations, it has the arabic of each hadith too. The search facility is also good as it allows you to search all books together. Each hadith has a permanent link so you are able to bookmark it and find it easily later as well as a link to report errors.
This is my second favourite, the website lists 12 collections (some incomplete) and some ahadith commentaries. You are also able to search all ahadith books all at once! Each hadith has a permanent link, useful for bookmarking and viewing/sharing with others. Reading ahadith from this website is different from all others that I’ve come across because it displays ten hadith per page whereas the others have it all listed on one page. The website also has a daily hadith section which shows a different hadith each day. Other features include a daily hadith widget which can be embedded on other websites, dua books such as Hisnul Muslim and the 99 names of Allah and many other features.
This website lists five collections which are complete, and has alternative translations the above two contain translations from darusalam publishers were as this one has translations by Ustadha Aisha Bewley. The site doesn’t have any visible search facilities and the ahadith are listed all on one page chapter by chapter.