I took a different approach from what many of the comments here recommend. Instead of weeding down my resume to recent and "relevant" experience, I emphasized the wide variety of projects I've worked on, and I listed everything in my LinkedIn profile, all the way back to my first programming job in 1969. I got rid of my traditional resume entirely and let the LinkedIn profile be my resume.
Also, I made up a new title/tagline for myself: "Low Level Full Stack Developer". At the moment, I'm the only person in the world with that particular description. :-)
I wanted to distinguish myself from the other common definition of "full stack developer", which often seems to imply somebody who is an expert on website scalability. That's not really my thing: I'm better at going down the stack into hardware and device drivers and such.
So I included some interesting side projects that were outside the usual web developer arena, such as PdfChip where I took a PDF datasheet for an ARM chip, connected it to a development board, and made the pinout diagram in the PDF interactive so you could see the state of the pins in the PDF, and click on pins to toggle them.
Then I started writing back to all the recruiters who had been pinging me, including the ones that were way off like the place that was looking for a "Drupal themer". Always be nice to recruiters; you never know when you'll need one. :-) And indeed, some of them also had more relevant opportunities.
And these conversations helped me in my thinking about what I was really looking for: something very different from the traditional web work I've been doing for several years - something more hardware oriented (and I don't mean just computing hardware).
I noticed that there were a couple of local biotech companies looking for full stack developers. Wrote to one and never heard a peep back from them, not even after a couple of followups. Wrote to the other and heard back from the CEO right away. Got together with the team a couple of days later for a fairly informal interview.
They didn't insult me with a coding test - they had already looked at some of my code, and the questions I've answered on Stack Overflow. It probably also helped that I had submitted a small but good quality pull request to one of their open source projects the day before. :-)
Had lunch with the CEO a few days later to work out some of the details, and they made the offer a few days after that.
I can't really disagree with the advice that you should focus your resume/LinkedIn/whatever on recent and relevant experience, and I used the introductory section of my LinkedIn profile to highlight those things.
But if admitting that my first programming job was in 1969 gives people a clue that I'm old, so what? They will figure that out when they meet me! I would rather work with people who see my 45 years of experience in a wide variety of projects and think it means they can learn something from me - just as I can learn some cool new things from them.