Tablets, including the iPad, are a great way to read digital comics, and the Apple App Store is full of apps to download comic books. Comics by comiXology is a free app that allows iOS users to access comic books from all the major publishers, such as Marvel, DC, Image and more. The app also offers a subscription service where users can read back issues of comics for a monthly fee. ComiXology Unlimited is actually limited in what you can read, so make sure you check its list of titles before subscribing.
Marvel Unlimited is another subscription service by Marvel Entertainment. The app gives users access to thousands of Marvel comics for $9.99/month. This also has an eight-month gap for current issues, so again, check the fine print before signing-up.
YACReader ($1.99) is comic book reader that supports many comic book files and import methods, such as DropBox, Google Drive and more.
All the major comic book publishers, and popular smaller publishers offer their own apps for downloading and reading comics. Here are a few links: