Pronunciation of tomato
<<And probably just about every European language.>>
No, actually many European languages do not have aspirated stops, but (most) Germanic languages do.
Is there a widely spoken European language that doesn't?
A good, well-known set of examples of European languages without aspirated stops at all would be the Romance languages.
As for Germanic languages, the only Germanic languages that I know of which lack aspirated stops are Dutch and presumably the other Low Franconian languages, Afrikaans and West Flemish. However, aspiration is used quite differently in Icelandic and Faroese from its classical allophonic usage in most other Germanic languages; for instance, Faroese will preaspirate "geminate" fortis stops but not aspirate word-initial non-geminate fortis stops.
<<Is there a widely spoken European language that doesn't?>>
Spanish, French, and Italian come to mind.
Then I don't get it. I can post an audio sample of a French word containing [t_h].
<<Then I don't get it. I can post an audio sample of a French word containing [t_h].>>
I don't get what you're saying. I've never read or heard of aspirated stops existing in French.
Kirk, Lazar, Travis:
Do you guys at least acknowledge the aspirated stops in the above recordings or am I missing something?
Russian does not have aspirated stops./
Spanish T's aren't aspirated. They aren't as diluted as the American alveolar flap, but they have a much duller sound than an aspirated T. And they ARE used at the beginning of words, like "tortilla" "tortuga" "todo" etc. It's a distinctive sound.
<<Do you guys at least acknowledge the aspirated stops in the above recordings or am I missing something?>>
Those did sound aspirated. But nonetheless, I've never read anything about regular aspiration being part of French phonology. It could be that there's a tendency to aspirate a final /t/ if you're emphasizing a word. We'll have to ask Greg.
As for European languages without aspiration, I'm pretty sure there's no aspiration in Spanish or Italian.
In French, it's common to hear aspiration with "u" as in "tu", "salut", "bu".