Does a Chinese character almost-always represent a word? My guess is that (at least) 99.9% of Chinese characters represent words.
The possible exceptions are 的 and 吗 -- as in:

的  in  &quot;my car&quot; (wǒ de chē)   我的车
吗  in  你好吗?  or   &quot;Ni Hai Hao Ma?&quot; (你还好吗?)

的 and 吗 may not be words, more like suffixes or (sentence) particles. Are there many more exceptions like these? Thank you.

The concept of a [Chinese word] is not too tricky. See:

Are there large discrepancies between what Chinese consider to be words?

What percentage of Chinese words are 1-character ? ... 2-character?

Also related:
Why do native speakers often say a character has &quot;no meaning&quot;?
的 is foremost a particle, but also a word in its own right. As de, it can mean plus, as in 七个的六个一共十三. As dī, it can mean cab. As dì it can mean target.

吗 is in ma and má likewise mostly a particle, but in some instances an isolated character without meaning of its own. As mǎ in 吗啡, it means morphine.

There are a number of such isolated characters, such as 蝴, which can only be used in conjunction with 蝴蝶, 蝶 in itself meaning butterfly.

蝴 is thus not a word, since it cannot stand on its own and doesn't convey any useful information. One could still infer the meaning from its written form, but likely not from speech (perhaps a child trying to say hú but not completing with dié, then).

This is true for a handful of such isolated characters. For instance 蚂 can be part of 蚂蚁 mǎyǐ, 蚂螂 mālang and 蚂蚱 màzha, but is not a word in itself. The same is true of 螂 and 蚱, which can be combined in words but not carry individual meaning. 蚁 can stand alone, as the family of ant-like insects.

Particles, on the other hand, can mostly be regarded as words, as they carry linguistic meaning in their own right. 哦 and other interjections are of this nature.