Well, let me try:
- Серый — boring, mediocre; semi-legal ("серый рынок").
- Красный — (obsolete, but fully understandable nowadays by any native speaker), beautiful: "Красная площадь", "красна девица". Moreover, historically it is its first, original meaning, only later on did it become a color indication, displacing червонный/червлённый; may also mean strong or exaggerated as in "красное словцо".
- Голубой — male homosexual ("голубая" for lesbian is inappropriate); relaxed in "голубые грёзы"/"голубая нега" (something close to dolce far niente); (rapidly becoming historical) television in phrase "голубой экран"; (historical, not understandable nowadays) gendarmes, police in tzarist Russia, in phrase "голубые штаны", check out also гороховое пальто.
- Розовый — in phrases like "жизнь в розовых тонах" or "смотреть на мир сквозь розовые очки" means rose-colored, (unduly) optimistic. Розовая sometimes is used for indicating lesbianism, but, compared to голубой is used much more rarer.
- Зелёный — greenhorn ("ты ещё зелёный совсем, куда тебе"); environment-friendly, ecologic ("зелёные технологии"); apathy, cheerless as in "тоска зелёная (drowsy boredoom, depression)". One can also turn green from anger ("позеленеть от злости"). In the late Soviet time, the American dollars were called "зелень" (green stuff) or just "зеленые". "Зелёнка" in military slang means woodland or dense thickets (in everyday use just Brilliant Green dye).
- Белый — (noun) I hate to say it, but it is heroin; legal ("белый рынок", "белая зарплата"); "белая ворона" ironically, this can be translated as "black sheep". "Белая зависть" (white envy) means that you are glad for someone, but also regret that you aren't like him/her, as opposed to "черная зависть" (black envy) when you are angry that the other person has something that you don't.
- Чёрный — illegal ("чёрный рынок"); villainous ("чёрное дело ты задумал"); dreary ("на душе черным-черно").
- Жёлтый — in the phrase "жёлтая пресса", which is a calque of "yellow press"; there is also derivative adjective "желтушный" and noun "желтуха" ("Вся эта статья — чистая желтуха"). In the phrase "желторотый птенец", it means a very unexperienced person.
- Фиолетово (as an adverb, not an adjective) — used to indicate indifference: "Мне это абсолютно фиолетово".
- Побагроветь (verb, derivative from "багровый") — to get furious, to get pissed off ("Валерий Петрович побагровел от возмущения"). Cf. also сделаться белым.
- Серо-буро-малиновый — colloquial description of a color that is hard to determine or that is a result of a strange medley of hues.
Political (ability to understand these depending on one's education and conversation context, although красные and белые are much more recognizable than others):
- Красные — communists.
- Белые — the White movement.
- Коричневые — fascists.
Also, an edit has been suggested to incorporate into this list the phrase малиновый звон, but be warned, this has nothing to do with the color малиновый. Much rather, this is a phonetical coincidence, much like Китай-город is by no means related to China.