Is there anyway to opt out of Wikipedia? Say, somebody created a profile page for me without asking for my permission. Is there anyway to delete my page?
In general, anyone can edit or delete Wikipedia pages.
If you are a "notable person" then you can expect your edits to be reverted, however; on the other hand, if you are not very notable, a page about you would probably not survive very long anyway.
My original question was: let's say I'm a well-known person in my field, somebody created a Wikipedia profile page for me, and the page has been there for years. Is there anyway to have it deleted?
No. Wikipedia itself does not grant you any special right to delete your own article page. You may have (IANAL) certain legal rights that would allow you force them to delete the entire page or parts of it, but this rarely happens.
Wikipedia isn't opt-out: you can't opt-out of being written about in newspapers if you do things that make newspapers want to write about you. Wikipedia doesn't delete stuff just because the subject doesn't like or want the article. (Plenty of politicians don't like the fact that the articles about them accurately report the things they've said that they now find impolitic.) But it may be the case that you aren't notable, in which case we should delete it.
Easiest thing is to email me - tom@tommorris.org - I'm an admin who has handled hundreds, possibly thousands, of deletion debates. My Wikipedia account is here FYI: https://en.wikipedia.org/wiki/User:Tom_Morris
Or you can email info-en-q@wikimedia.org and you'll get an email from someone (possibly me) who is an experienced Wikipedian who'll be able to have a look at the article and sort out any issues therein, put it under protection if there's been vandalism etc. or nominate it for deletion if it doesn't meet the notability requirements.
You can generally get the page deleted only if it doesn't meet their criteria for a biography of a living person. Asking permission or being acceptable to the subject aren't in the criteria. See:
Let's say I'm a well-known person in my field, somebody created a Wikipedia profile page for me, the page does meet their criteria for a biography of a living person and the page has been there for years. Is there anyway to have it deleted?
If you are a "notable person" then you can expect your edits to be reverted, however; on the other hand, if you are not very notable, a page about you would probably not survive very long anyway.