This is not really a hard thing to work out. First, of course, is Showcase #4, the comic that started the superhero revival that is probably the biggest aspect of the Silver Age. To give you an idea, during the 1950s, DC Comics published 3,397 different comics, of which 849 were superhero-oriented (including Lois Lane and Jimmy Olsen). In the 1960s, DC published 3,579 different comics, of which 1,629 were superhero-oriented. The return of the Flash kicked off that surge.
Next up is Adventure #247, which introduced the Legion of Superheroes:
The Legion was one of DC's best features during the Silver Age. The combination of a futuristic setting with super-powered characters proved irresistable to readers of the time and provided seemingly endless plot possibilities.
The third major DC comic of the Silver Age is Brave & Bold #28. Now that DC had brought back Green Lantern, DC combined him with the Flash, Martian Manhunter, Wonder Woman and Aquaman into a fighting team called the Justice League of America. This served as a marketing gimmick for the individual magazines featuring those heroes (although at the time both Aquaman and Martian Manhunter were backup features in Adventure and Detective respectively), but it also apparently sold very well on its own, leading Marvel Comics' head honcho Martin Goodman to instruct Stan Lee to create a superhero team, which of course became the Fantastic Four.
The next major DC comic of the Silver Age may not be as apparent as the others, but it's a key to understanding the appeal of the superhero titles during this era:
Prior to this, DC had reprinted almost none of their older stories. Superman Annual #1 gave recognition to the fact that comics had a back story that it was important to understand in order to get the most out of current issues. It also represented a promise from the editors to you, that if you didn't know the back story, DC would fill you in over the years with reprints of their older tales. DC did a phenomenal amount of reprinting in the 1960s and early 1970s. Even Marvel got into the act once their comparatively recent tales were old enough to attract new readers.
The final major issue is obvious:
In the very first appearance of the Flash in Showcase #4, we learned that Barry Allen had read comics featuring the Jay Garrick Golden Age Flash. So it seemed only logical to pair the two up. But there was a problem; Jay Garrick (the gentleman on the right) had been a fictional character only on Barry Allen's Earth. The solution hit upon by Gardner Fox was to postulate an alternate Earth, called Earth-2, where the Golden Age superheroes had reigned.
This opened the door for a slew of Golden Age/Silver Age crossovers, about which I have a post planned for the future. It also created numerous headaches for DC's editors as time wore on, but that was not apparent in the 1960s.
Other comics that were crucial to the Silver Age DC, but perhaps not as critical as these:
Showcase #22, featuring the origin of the Hal Jordan Green Lantern. Lost in the memory of the Silver Age is the fact that it took three years after Flash's debut issue for DC to bring back its second GA hero in a new form. After this the pace quickened, with Aquaman, Atom and Hawkman all getting new launches.
Detective #225, with the first appearance of the Martian Manhunter, which actually predates Showcase #4. However, MM was a new character, not a rebirth of an old one.
Detective #327, with the "New-Look" Batman. Certainly the Batman TV series had a huge impact on DC Comics, but it is hard to say that this really spawned the show. Indeed, it is arguable that far more influential was Batman #155, which started the practice of bringing back Batman's Golden Age rivals (in this case, the Penguin).
Action #242, with the introduction of Brainiac. This is arguably the beginning of the Silver Age Superman under Mort Weisinger, although his name would not appear as editor for another few months. Weisinger's tenure running the Superman books was extremely influential, as he standardized the looks and mannerisms of the characters and presided over a substantially more serious hero than had been the case in the past. Superman in the 1940s and 1950s, perhaps influenced by Captain Marvel, had a touch of whimsy to it. Under Weisinger most of that was gone (with the notable exception of the Lois Lane series).