Do you socialize online with your realm mates outside of the game? Does your realm even have a coherent realm community on the web or in social media? At its most basic, players from a given realm can socialize to some degree on Blizzard's official realm forums, although I'm sure you've discovered how chaotic and contentious most of those forums are. If you suspected there simply has to be a better way, you're right -- and many realms are enjoying them.
As it turns out, a number of realms have created freestanding realm web sites where players pull together to chat and coordinate special events, roleplay, charity fundraisers, holiday events and more. Roleplaying realms such as Argent Dawn (EU) tend to lead the way with fully developed web sites, a logical resource for coordinating complex, multi-guild storylines and events. Feathermoon's magnificent Feathermap.net practically begs players to get involved.
Facebook is home to relatively small but socially active realm communities. Argent Dawn (EU) boasts an active page here to augment its web site. Other realms that use open or closed groups or public pages on Facebook include Darkmoon Faire (EU), Draenor (EU), Gnomeregan (US), Moon Guard (US), and Zangarmarsh (US).
You can find your realm mates on Twitter, too, such as @Ghostlands_EU.
Has your realm organized on its own web site or on Facebook or Twitter? If so, are you plugged in? Share your favorite realm's web site, Facebook page or group, and Twitter account or lists in the comments so the rest of us can join in!