I have written a manuscript and want some feedback from experts. So I sent emails to different professors to ask their permission if they want to view my manuscript. I did not attach my manuscript to my email. Would it be considered spam? Would it ruin my reputation?
How are you going about it?
If you blast a generic email to 100 groups that are approximately in your subfield, I would not expect a great outcome. Most people will ignore it; a few might be annoyed, especially if a) they perceive the paper as low quality or irrelevant to their work or b) multiple people realize they received the same email. I doubt this will have severe, longterm consequences, but it certainly wouldn't help.
On the other hand, you could certainly send a few targeted emails asking for feedback. This will work best if you identify people who are very likely to be interested in your work and explain why in your initial email. The authors cited in your paper might be a good place to start. I would consider asking a grad student or postdocs as well; I think you're more likely to get a response and it may be more in-depth too! It wouldn't hurt to ask for feedback on specific parts of the paper too. For example, I think an email like this would work reasonably well:
Dear Dr. Eisenhardt,
I am Ignus Ignatius, a 5th year PhD student in Dr. Xavier's group at State University. I enjoyed your 2008 paper about color matching in very young children. We adapted that paradigm to study color preferences in baboons and have collected some data demonstrating that they, like humans, have color preferences that vary throughout their lifespan. I'm currently writing this data up for the Example Journal, and would appreciate any feedback you might have.
Our preprint is here [link to reputable preprint server/website]. I am also presenting this work at next month's Hypothetical Research Conference in Springfield.
I would be particularly interested to know whether you think we have correctly controlled for interactions between colors' hue and saturation, as I know that was a focus of your followup work. We would be happy to recognize your feedback in the Acknowledgements of our next version.
-- Ignus Ignatius
If your field uses them, I would consider posting the manuscript to a preprint server, rather than attaching it directly. This sidesteps @NuclearHogie's concern about security, expands the potential pool of readers, and prevents anyone from "scooping" you. One potential downside of this approach is that if you solicit comments from someone, you should acknowledge their efforts somehow (formal acknowledgement, or even coauthorship), and doing so will likely preclude them from serving as a peer reviewer. Good luck!
This might be considered spam, but it might also be considered okay, especially if you have worked with a mentor or advisor to get your paper into excellent shape first. When I was a grad student, my advisor encouraged me to send a copy of my first paper to researchers whom I didn't know. (My advisor did know them.) More recently I have received, and replied to, emails with unsolicited manuscripts from student researchers.
If you go this route, I'd recommend that you (1) make sure your paper is immaculate, and typeset in the same way as other papers in your field, (2) have it read by someone at your home institution first; (3) attach your manuscript with your initial email; (4) be happy if you get one reply, and don't expect a longer back-and-forth.
If you are claiming a solution to a famous open problem, then your claim is very unlikely to be believed and your paper probably won't be read. If your paper is on a niche problem in an active area of research, you are more likely to be taken seriously.
Above all, accept that these professors don't have any obligation to you. Some might write back, but they're not being rude if they don't, so don't send any follow-up or reminder emails.