Amazon.com (AMZN 0.80%) made news last month when it struck a deal with Time Warner (TWX) to add select HBO content to its Prime video service. Beginning on May 21, Amazon Prime subscribers will be able to stream many of HBO's most critically acclaimed original series. If they own a FireTV (or any of the other set-top boxes capable of receiving Amazon's content), they'll be able to watch them directly on their television set -- no HBO subscription required.

In recent months, Amazon has signed several such exclusive deals, but the agreement with Time Warner generated a far greater degree of buzz, and for good reason: Time Warner's premium network has created many of the greatest series in the history of television.

Even though Amazon's deal doesn't cover currently airing shows like Game of Thrones, HBO's catalog is chock-full of quality programming. If you're a Prime member who hasn't always been a loyal HBO subscriber, here are five shows you should check out.

The Sopranos
This was the show that started it all. It wasn't HBO's first original drama series (that would be Oz) but it was its first breakout hit, and it established Time Warner's premium network as the place for quality television.

Nearly all drama series released in the last decade, particularly those featuring a male anti-hero in the lead role, owe a debt of gratitude to The Sopranos. If it wasn't for Tony Soprano, there might not have ever been a Walter White, a Dexter Morgan or a Frank Underwood. While it remains as entertaining as ever, fans of television who haven't yet seen The Sopranos should check it out, if for no other reason than to better appreciate its legacy.

The Wire
The Wire isn't for everyone. Many people will find it slow, drawn out, and to some extent, boring. Put simply, The Wire lacks the sort of dramatic hooks found in shows like Breaking Bad and Game of Thrones.

But its dedicated fans are numerous, passionate, and outspoken, even years after its conclusion. Run into one of these Wire fanatics, and they're likely to tell you it's the greatest show in the history of television. User reviews on Metacritic, a review aggregator, are overwhelmingly positive. Professional critics are a bit more mixed, but if you're open to an exceptionally well-acted cop drama, The Wire could become one of your favorite shows.

Six Feet Under
Part drama, part black comedy, Six Feet Under is a unique take on the traditional family sitcom. Over its five-year run, it won Time Warner nine Emmy awards and three Golden Globes.

Six Feet Under's showrunner, Alan Ball, wrote 1999's best picture winner American Beauty. If you've seen that film, then you'll have a fairly good idea of the themes tackled in the show. In terms of acting, Six Feet Under's ensemble cast includes Michael C. Hall prior to his role in Dexter.

Unfortunately, critically acclaimed shows often lose their way, concluding with disappointing finales that frequently upset fans. Six Feet Under is a notable exception -- its final episode is commonly cited as one of the best finales in TV history.

Deadwood
Both Six Feet Under and The Wire had five seasons; The Sopranos had six. Deadwood only has three -- earning it a top spot in TV Guide's list of shows that were canceled too soon.

It's also unique in that, unlike those other shows, which take place in the present time, Deadwood is a western, set in the 1870s. It won Time Warner eight Emmy awards and one Golden Globe.

Band of Brothers
HBO has released a handful of great miniseries over the years, but none have been as well-received as Band of Brothers. Produced by Steven Spielberg and Tom Hanks, the 10-part show follows a group of American soldiers during the second world war.

Band of Brothers won six Emmys, one Golden Globe, and a Peabody award in 2001, the year it was released. It has been universally praised by critics and viewers alike, and tops IMDb's list of the top-rated TV series.