Animal X - one of my first inspirations
Trystan L. Bass - whimsical costumes and accessories of all kinds. Also home of the Gothic Martha Stewart pages!
Katherine Caron-Grieg - historical costumes and event photos
Bjarne Drews - jaw-dropping embroidery and 18th century costumes
Melissa Heischberg - sempstress.org, Elizabethan focus with articles and dress diaries
Sarah Lorraine - historical costumes, beautifully detailed dress diaries
Lynn McMasters - mostly Elizabethan, with a terrific line of hat and accessories patterns
Rosiel - Cosplay designs with great attention to detail
Sarcasm-Hime - Cosplay and original designs
Kendra van Cleave - primarily historical costuming and excellent research, with a superb list of links
Costume-Con Visual Archive - photos of costumes presented at Costume-Cons from the beginning! Not really research, I guess, but inspiration!
The Costumer's Guide to Movie Costumes - screenshots, photos, and breakdowns of many costumes from historical and fantasy movies
The Elizabethan Costuming Page - Enough said.
The Great Pattern Review - from the Greater Bay Area Costumer's Guild, user-submitted reviews of commercially available costume patterns
Lord of the Rings Costume Research - if you can't find a starting point for your LOTR costume here, you aren't looking
The Padawan's Guide - sister site to the Costumer's Guide, focusing on costumes of the Star Wars saga
Pride and Prejudice Costumes - examines Elizabeth's costumes from the 1995 and 2005 filmed versions of "Pride and Prejudice"
The Regency Fashion Page - fashion plates, portraits, photos of extant garments
The Renaissance Tailor - Research and tutorials, Renaissance focus
Amphigory - reliable source for quality base wigs and cosmetics
God Save the Queen Fashions - Catherine runs a great drag shop out of Atlanta, and she makes beautiful custom costumes to order.
Patterns of Time - all kinds of historical patterns, great turnaround. Only catch is that it can be hard to tell which patterns come from which companies, which can make a huge difference.