In English we capitalize proper nouns [1] and we also capitalize adjectives that are derived from those nouns:

I'm going to London.
He's a Londoner.

This leads some people to want to call them "proper adjectives". The problem is, this is just a capitalization convention. We capitalize "Londoner" but wouldn't capitalize "lowlander" because one is based off of "London," which is a unique place (and so gets a proper noun), while the other is based off of "lowlands," which there are many of. That distinction is pretty weak when extended to the adjective: there are lots of Londoners and also lots of lowlanders.

Another way to look at it would be to consider words that are only capitalized or not because of historical accident. People from Indiana are "hoosiers", and this isn't capitalized because it doesn't have a companion proper noun. If by some quirk of history, however, they had come to be called "Indianians", the derivation from "Indiana" would entail capitalizing it. We'd say:

Heather's a hoosier but Owen's an Ohioan.

If English were a spoken-only language, proper nouns would still be a reasonable category, but proper adjectives wouldn't be.

(Scrabble neatly sidesteps this question by ignoring the idea of propriety and simply saying that "words that are spelled with a capital letter cannot be used.")

2013-08-15: Several people pointed out that my examples here are nouns and not adjectives. That was sloppy; sorry! The capitalization convention in English is for proper nouns and any derived adjectives and nouns. While the examples above are all non-proper nouns, the same thing applies to adjectives:

I love Gothic architecture.
I love classical architecture.

There's no difference in usage between adjectives like "classical" that aren't derived from proper nouns and adjectives like "Gothic" that are. If over time English speakers forgot that there had been Goths but kept the adjective to describe the kind of architecture, we would probably stop capitalizing the word.

[1] Though some nouns ('universe') are linguistically proper but not generally capitalized while others ('Xerox' in "my Xerox is broken") are capitalized but not linguistically proper.