I have never seen (or realized) an example of an academic website which displays ads.
I am thinking of a website not hosted by the institute, but as a personal website, paid by the faculty member.
Does it look weird/unethical/unacceptable if a person uses a service similar to AdSense for their website?
Such a website is itself an ad: for the lab, the lab's research, and for the personnel running/working at the lab.
In many ways, a lab website is like a resume. While it's not unusual for newsletters published by some local org (say, a school, church, youth group, etc) to have local ads to cover publishing costs from the neighborhood dental clinic, grocer, etc, but you wouldn't expect to find these on a resume.
Probably most people are conditioned enough to online ads that they wouldn't even notice them, but if they did it might seem a bit weird, and if they were at all intrusive it would be downright ugly looking and reflect badly on the lab. If I were working in a lab where the PI had a website with ads, I'd be embarrassed by it even though it wasn't my own responsibility. If I was visiting such a site, I might wonder if I've stumbled on some illegitimate content farm site by mistake.
I doubt a typical academic's website gets anywhere near enough traffic to make ads make much sense financially. The cost of potentially putting off a precious visitor doesn't seem worth it to me to pocket a few pennies.
If the site is hosted by the university or with any grant funds for research it is likely illegal or against some terms to make any personal profit off such a site; even if the funds are just used to pay back the site costs it's a gray area that is still probably not allowed. A university could certainly even have a policy on this even if their funds are not directly involved if anything about the website affiliates it with the university, including being an official or pseudo-official website for a lab operating out of that institution.
It's just not worth the potential conflicts from any angle I can see.
I'm not quite as negative as the other current answers here. I don't think it is unethical, for example, provided that the domain is your own. Weird, perhaps.
But, a warning. Don't sign up with some ad "service" that has the ability to place ads on your site according to their judgement, not yours. You will regret it pretty quickly, I'd guess.
However, there is unlikely to be any financial advantage to you unless you have a blog with millions of readers. And most of the folks I read (blogs) have periodic campaigns to solicit contributions. But they are also "in the business" of writing daily on subjects of interest to a wide audience.
Of course, academic authors often have "ads" on their web sites to enable potential readers to find their books. I doubt that anyone would object to that.
I don't think I would call it "unethical," but certainly weird and borderline unacceptable.
While I'm sure the idea is to just recoup server costs; it would strike me as very weird to try and profit off visits to your personal website and I would probably avoid visiting it again.
If you were being interviewed, I can't see it being a positive.
Also keep in mind the ads may be targeted. I don't think someone seeing a male enhancement pill on your website would be very impressed, even if it was their own search history that suggested it.
As Brian said before, there is not enaugh traffic on an academic website. However, I don't think it would be unethical to show ads (if you can filter out what kind of ads shouldn't appear on your website). I think that in academia, we are primed to think that we shouldn't think about profit. If someone can make a good profit with ads on his/her webpage, it is alright for me. I would rather look at the papers to judge professionalism.
Yes, it is so weird to show ads on academic websites. But it wouldn't be enough frustrating if your ads are not inappropriate or other than interest-based but honestly, sometimes interest-based ads flow my mind to that ad's content rather than what and why I could open that website! So, this is also an awkwardness of ads.
It likely depends on what you consider to be "ads".
Some might argue that the entire website is an advertisement for the university. If you've ever sat in meetings with the alumni association, student recruitment, and the university's "development" department (the people who try to get you to donate money) to redesign the university's website, you'd know how obsessed they are over 'branding' and the like.
But even if you consider them to be a business (even if it's a real estate business that's obligated to teach classes), you'd understand their focus on branding and such. You wouldn't expect to go to ford.com and see advertisements for other vehicles show up ... you might see ads for Ford vehicles, but they want to control their brand. Looking at my alma matter's website just now, I found a few pages with ads for 'online giving'.
It's possible that a school might have a "Code of Conduct" or similar that specifically forbids monetization of web pages, especially if they're a non-profit. There may also be concerns about third-parties harvesting information about their staff and students. If a third party knew who was viewing which websites, they might be able to infer who were students and what courses they were enrolled in ... which may be a FERPA violation. (I'm not aware of any lawsuits / decisions on the matter, this is just speculation).
But we still get into the question of what qualify as "ads". You used to see a lot of groups that participated in "rings" where there would be some topic of unifying interest, and then sites would join the ring, giving links to the other participating sites while getting links back in return. So you had "ads" to link to other thematically linked web pages, but it wasn't like today's ad networks where you had absolutely no idea what might show up on your page.
As has already been alluded to by others, this is bad for the university. If their servers get used for a "watering hole" attack, it could lead to the site being blocked at firewalls for the federal government, which is really bad for research institutions.
You also get the occasional link to a sponsor's page. Usually it's just a text link or maybe a logo and link. You might see this on departmental webpages or various student organizations. There were a number of engineering competitions at my university that I believe all had corporate sponsors (solar car, concrete canoe, baja SAE, etc.)
There will be increasingly higher levels of flexibility and autonomy as you move from the "main" university's web pages to departmental pages & sites to organizations and personal (staff, faculty & student) sites.
These days, if staff or student wanted to monetize a website, it's easy to get external hosting. You wouldn't get shut down when academic computing decided to look into why the webserver was bogged down and found that a staff member had set up a porn site. And you can more easily move your content elsewhere if you control the domain name.
In general, it's just bad form -- does your page exist to give out authoritative information, or to trick people into visiting so that you can try make money off them and try to get them to go elsewhere? Webrings or other link exchanges might make sense in some specific cases, but things like AdSense and such make your website look unprofessional as you lose control over your page. The university provides the hosting, so it's not like you're trying to make your cost back for hosting the pages.
(note: I was the webmaster for a large private non-profit university in the 1990s. I have no idea how many people these days bother w/ university hosting vs. just having a facebook page. And yes, we really did have a staff member put up a porn site. He even worked for our department (night shifts on the helpdesk), and lots of our co-workers had complained about him, but management kept ignoring them)
A major cause why conspiracy theories, fake news, and bad science is so prolific today, is because it's profitable. The recipe is simple: create a website which pretends to be a newspaper or an academic site. Monitor the current news, and then write an article which states the exact opposite. People will share the "shocking discovery" on social media, their followers will click on it, and then the creator of the site earns money from the ads, especially if they get lucky enough and their article becomes viral.
You really don't want to create the image in your readers that you are operating such a site.
