I'm 25 (years old)

When you say "I'm 25" to mean that you're 25 years old, would you consider "25" a noun or an adjective?

Neither. Twenty-five is a numeral. In your example sentence, 25's syntactic role is that of a predicative.

I wish Wikipedia would get their act together.

As well as claiming that numerals form a word class (in Armen's link) they claim that numerals form a subset of the determiner word class ( http://en.wikipedia.org/wiki/Determiner ):

A determiner is a word, phrase or affix that occurs together with a noun or noun phrase and serves to express the reference of that noun or noun phrase in the context. That is, a determiner may indicate whether the noun is referring to a definite or indefinite element of a class, to a closer or more distant element, to an element belonging to a specified person or thing, to a particular number or quantity, etc. Common kinds of determiners include definite and indefinite articles (like the English the and a[n]), demonstratives (like this and that), possessive determiners (like my and their), and quantifiers (like many, few and several). Most determiners have been traditionally classed along with adjectives, and this still occurs: for example, demonstrative and possessive determiners are sometimes described as demonstrative adjectives and possessive adjectives respectively. However, modern theorists of grammar prefer to distinguish determiners as a separate word class from adjectives, which are simple modifiers of nouns, expressing attributes of the thing referred to. ...

Types of determiners

Articles Demonstratives Possessives Quantifiers Numerals Distributives

[bolding mine]