On the third Thursday of the month, the “Best Damn Happy Hour” (their title) has live DJs, mini golf, board games, giant Jenga (TIMBERRRRR!), and deals on cocktails and food at the many eateries inside the Armory, the food-court-ish building at Seattle Center (21+ only). No cover.
Behemoth SODO wine emporium Esquin offers free wine tastings every Thursday and Saturday, with themes like "92 Points and Above," "Viva Argentina," and "Under $10 Specials." Sometimes winemakers join in, and snacks are not unheard of. Check their website to find out which wines they're uncorking. Free.
Slosh down Post Alley for the Thursday Wine Hop, where $4 glasses of unspecified wine are served from 5 to 7 pm at Kells, Post, the Tasting Room, and the White Horse Trading Co.
West Seattle Cellars hosts an informal, regionally themed wine tasting in its little house on California Avenue every Thursday. When the tasting coincides with the West Seattle Art Walk (on the second Thursday of every month), it's partytime. Check their website to find out which wines they're uncorking. Free.
Every Thursday and Saturday, Vino Verite hosts a casual wine tasting that will not part you from any of your money. Free.
Geeks Who Drink is a company that hosts trivia quizzes at different bars every damn day of the week, here in Seattle and all over creation, usually free (except for bar owners, who pay a "reasonable" rate). Starred for geeks who drink who like pub trivia.
Literally millions of happy hours are taking place around Seattle RIGHT NOW. One is highly likely right under your all-too-sober nose: Find out where it is here (for iPhone users) or here (for Luddites). Food! Drinks! Cheapness! Yes! CHEAP!.