"Invisible" thread -- it really looks like extra thin fishing line; great for small detailing, applying trim, fixing 'mess ups' (admit it, we all have them)... And best of all it matches any fabric!

Stop Fray -- a liquidy, clear glue-like substance, very important for materials that fray easily otherwise such small seams can come out; comes in small bottles in most craft areas (I got mine at Walmart); the price may seem steep for such a small amount, but it really goes far, I still haven't had to replace mine

SHARP Scissors -- I like Fiskars. If your scissors are too dull it can cause your fabric to 'pull' while cutting, making your pattern shape untrue. Plus it adds all the more struggle to your project to have to be 'chewing' at material. I also like keeping a pair of tiny "sewing scissors" around (they're about 3 inches long) for snipping thread or cutting out something very intricate

Various Closures -- snaps, velcro, hook-and-eyes, small zippers... Some are better for some fabrics and patterns than other (and I even choose mine according to mood sometimes, so I like to have a variety on hand) or sometimes in combinations of more than one type

Remnants -- visit the remnant section of your fabric department/store and keep plenty on hand; they're usually cheaper anyway

Imagination! -- This is very important. Most costumes, even with patterns, take great imagination for them to turn out. I cannot ever rely completely on a pattern. There are always needs for variation. And the look you get as a final product is greatly reliant on what you have pictured before starting--the color, the style, any extra 'flounce' or accessories... If something messes up, there are so many different ways to try to fix it! Remember to 'think outside the box'. There's never one right solution to anything in sewing.