For people who are looking to try a variety of manga, a number of websites offer free previews, but more importantly free volumes of a whole range of titles.
Each website offers different options, and often uses its own proprietary reader, even if the titles are the same. So, it makes sense to do some exploring before deciding which one(s) you prefer as a go-to source.
In my case, I sample here and there, but because I am limited to using a US credit card, there are only a few options for me to actually buy digital copies of the manga that I want to read.
I have been using eBookJapan the longest. It has made some changes recently by merging with Yahoo! Japan so that Japanese folks can use Yahoo! Japan money, but I am still able to use a US credit card.
BookWalker is another site that I have looked at this year. It includes manga, light novels, novels, nonfiction, game strategy books, and interestingly enough doujinshi. There is a sister site called BookWalker Global for the English translations of manga and light novels. So, flipping between the two can really be useful if you are the type who wants to read first in English before dipping into the Japanese (or vice versa). There are lots of manga that are available for free for a limited amount of time.
Now the BookWalker Global website does allow payment by PayPal. There are also notes about licensing restrictions (the English language editions not allowed to be sold in Japan) And if you are wanting to look for the Japanese original of a manga/light novel that you enjoyed, look at the product details towards the bottom of the page.
CMOA is an example of a comics/light novel website that offers a monthly subscription to either unlimited or limited (missing BL, TL, light novels aka the good stuff) but only accepts credit cards issued in Japan. So, that lets it out for me. BUT, there is a free login option that you can use to either read through the browser or use the reader. The reader (bookshelf) application is available for Windows, iPad, and Android.
If you want to use the website for research – looking at rankings, genres, etc. The categorization is pretty good and I really appreciate the adaptation (which titles have been picked up for anime, movies, dramas) information.