Attachment or no attachment? I am currently applying for a PhD position and have emailed many professors. My emails often include a general introduction and my CV plus a research statement is attached.
I try to be brief in the email text, as I know professors get tons of emails like mine and don't have time to read a long one. That's why I just mention my interests in the body with the reference to my research statement for the detailed explanation.
Up until now, the replies were only about positions, funding, etc. But today I got an email expressing this about the email itself:

I recommend that you briefly describe the focus of your research interests in an e-mail (main body, not as an attachment) when contacting a suitable member of staff in order for the staff member to assess their suitability as a potential supervisor in that area.
[...] As a principle, we do not encourage sending e-mail attachments in initial correspondence, as a public institution we receive a lot spam and potentially harmful e-mails with attachments.

I was wondering, is this the prevalent routine that I should consider for my emailing other institutes/professors as well? Or is it just their principle and others' may differ?
The writer of that response has given you a valuable clue.  If, having read the email body, the recipient does not already have an active interest in working with you, the recipient is very unlikely to look at the attachments.

Instead, include a short paragraph about your research interests and a short summary of your CV  in the body of the email and offer to send details if requested.