Google has demonstrated exploiting the Spectre CPU attack remotely over the web:

Today, we’re sharing proof-of-concept (PoC) code that confirms the practicality of Spectre exploits against JavaScript engines. We use Google Chrome to demonstrate our attack, but these issues are not specific to Chrome, and we expect that other modern browsers are similarly vulnerable to this exploitation vector. We have developed an interactive demonstration of the attack available at https://leaky.page/ ; the code and a more detailed writeup are published on Github …