Not too much, but enough to make it appealing. The name of the site and a link to it, of course, but beyond that, just a few details that would describe the site and explain its purpose and maybe a little picture that's relevant to the site to help bring that visual in. If the site has any social media presence, including information about that would also be helpful.
I do keep bookmarks when they're given to me, but I don't use a good chunk of what I have because I have so many and I just use one until it's so worn, it just needs to be trashed lol. But I would be more likely to keep a bookmark and use it, even if it was several years down the road, than say, a business card that I would more than likely just toss after giving it a quick glance and maybe taking a peek at the social media if anything is on there. I know a lot of times, I've looked through business cards I've picked up at events and I'll go on their social media accounts, and I'll follow those, then toss the card and forget about it until I'm browsing the social media later.