I still have my VHS and Hi8 tape players (even my old Videonics separate video editing boxes), and I have a camcorder with firewire (it uses mini-DV tapes) and S-video/composite pass-through, as well as a firewire input on the computer. So I hook up that camcorder to the computer via firewire, then I hook the tape player to the appropriate connection on the camcorder. There are analog video capture boards (and other devices) available to do the same thing.
Then I fire up Pinnacle Studio and use its capture mode to get the video into the computer. With Studio I can make DVDs and I can make .mp4 files (or several other formats) to play on the computer.
I also have a DVD player/writer with analog inputs for direct transfer to DVD, but it's not as versatile as doing it through Studio.
I have a Plustek 7600 slide scanner and have put probably a third of my 10,000 plus slides into the computer. I still have a cassette deck and an open reel tape deck, too, as well as a good turntable, and have copied a number of my LPs, open reel tapes, and cassettes to get them on CD.