I have a lot of Goodwill experience, and other thrift shop experience too.
Whether they pick up or you have to take it to them depends on the regional policy. Here, while some charities pick up, Goodwill does not. However, in my experience (think I could work that word in a few more times?), the places that pick up tend to reject far more stuff than the drop off charities. My theory is the guys loading the truck are 1) not really qualified to judge what will sell in the store, 2) not happy about lifting anything over 20 pounds. More than once both VOA and Salvation Army (which pick up) have refused items which I dropped off at Goodwill, accepted by a human rather than deposited in a donation bin.
Here, Goodwill does indeed take VHS tapes (and music cassette tapes as well, even vinyl records) and VCRs, but will accept computers and their components only if they're less than 5 years old. However, if you've got a working computer to get rid of, wipe the drive clean and put it in the "Free" listing for your city's Craigslist. Someone will want it.
Maryn, going to Goodwill today, as a matter of fact