Can't get older than this one:

https://info.cern.ch/hypertext/WWW/TheProject.html

I give you Warren Buffets company website.
https://www.berkshirehathaway.com/

The domain was purchased in 1996 It looks like they never updated the layout since.

Everything is possible at Zombocom, est. 1999

Everybody get up, it's time to slam now! We got a real jam goin' down now!

Welcome to the Space Jam

GameFAQs.com launched November 5, 1995, although it didn't have that name or URL until 1996.

Honourable mention:
https://homestarrunner.com/

Webtender - An On-Line Bartender.

The Webtender web site including, but not limited to the collection of recipes, web links and drinking games, as well as graphics and layout, is Copyright © 1995-2025, The Webtender/Pål Løberg unless stated otherwise.

https://www.webtender.com/info/c.html

Not only is it 30 years old, but it has searching built-in since at least 1997, if not the whole time. This puts it in a very special class: first-generation server-side web applications. Looks like it's still rocking cgi-bin.

Peter's The Evil Overlord List is a treasure of the long before times: http://eviloverlord.com/

Copyright 1997

"The Top 100 Things I'd Do If I Ever Became An Evil Overlord"

Mandatory reading for anyone trying to be an Evil Overlord.

No idea why this is the 3rd time this has come up now, but I just learned this year that an anti "barney the dinosaur" webpage is among the oldest still active ones, where you can shoot and stab him.

Hate for children's media for being... for children has really come a long way. Now we hate them for legitimate reasons, like peppa pig for being bloody monarchists and Bluey for being Australian.

https://netbsd.org/ registered March 1994

https://perdu.com/ registered June 1996.

Does SDF count? It's been going since 1987. Obviously the Lemmy instance is newer, and it's stretching the definition of website a bit.

https://zorotl.com/

The official page for the alien in the "I'm Blue" music video.

https://info.cern.ch/

theguyintheglass.com (about the poem) was last updated on 1998-10-03 and created on 1997-12-25 according to the footer.

http://thebear.org/

This still exists. It's Grateful Dead related.

I don't know how to find any date info on it though, sorry.

I recently had to dig deeper into Regex than I thought one could dig into Regex and found this website that claims it’s from 2003: https://www.regular-expressions.info/

The oldest one I regularly use is this one: https://web.archive.org/web/19961108115333/http://www.kela.fi/

It's the Finnish state organ for giving people their welfare benefits and operating the national health insurance system. So, if you get a child, you get an amount of money per month from Kela for having a child. (Because they want the population to grow).
Or, if you end up unemployed for a longer time, it's Kela that will pay your unemployment benefits.
Of if you break your leg, it's Kela that pays for your hospital care. I don't know how many forms I've already filled on their website :D

But yeah, the site's been around for a while now.

Lost Souls Domain

It's surely one of the first sites that I know and use, and it's still alive. I think it's from the 90s. (Looked it up again, their earliest visitor count starts at 1997)

Later we have Metal Archives, but I think Lost Souls Domain was the first website where you look for Metal music informations.

My MySpace page. Has ALL the animated dancing banana GIFs you could ever want.

Sluggy Freelance and Schlock Mercenary have both been around a while and both have (or had, when I still had time to read webcomics) stellar reputations for reliability.

I was going to mention User Friendly, but sadly that appears to be down. I think it was last time I checked, too, so I'm guessing it's a lost cause.

I have a website that has been up since 1995. I haven't updated in 20 years or so.

https://milk.com/

1994, and still quite active

http://www.kaillera.com/

This is still operational. Early middleware for online multiplayer in video game emulators. I'm surprised to see a few still use it.

Edit: 2001

Yahoo.com always comes to mind for these.

March 1994

www.crazyguyonabike.com is an old one that is still running.

Oliviatremorcontrol.com

No idea the year but it’s a band website that still has Web 1.0 vibes

For websites I actually use, even if just every once in while:

Shadowlord Inc.

The website, according to it and wikifur was founded in 1999 ( allegedly September 23rd according to the website ).

If you like things like transformation scenes in media, this is a site for you. Still being updated to this day. Does have some 18+ stuff, but you'll know right away that it is because they have the thumbnail for that clip tell you it's "R 18+ RESTRICTED".

Edit: just found out you need an account to access restricted R 18+ content... So to you'll be safe enough from that content.

serebii.net is one of those sites that surprises me that not only its still up, but also being regularly updated.