It depends on what kind of quality you're trying to preserve, and how much you're willing to spend. A straight conversion could be done really cheap, but you probably won't be happy with the results.

For VHS to DVD (or other digital format) - The hardest part is converting the analog tape to digital (A to D). You could spend tens of thousands of dollars in equipment to do this right. However, since VHS itself isn't the best quality to start with, it doesn't really make sense to try keep everything at such a high quality. There are cheap converters out there (around $100), and it could be done on a regular computer, but the results aren't great if you are concerned about quality. A easier way, if your'e willing to spend a little bit more money, is to get a Mini-DV camcorder with auxiliary inputs, then use the camcorder itself as a A/D converter. You plug your VCR into the camcorder, and either record it to digital tape or run a pass through directly to a computer as an .avi file. If you do record to a computer, you will need one fast enough to capture the video real time, which most modern computers should be able to do. Once it's in digital format, it's failry easy to transfer or convert to other formats. I prefer this method, for one, you will always have a high quality digital backup of the video (on mini-DV tape), and two, you have a camcorder you can use for other things rather than a dedicated video capture board on a computer.

For converting slides, if quality isn't an issue, you can actually project them onto a screen and take digital snapshots of each one. I've actually used this method to transfer old reel to reel movies to a VHS, it turns out ok. The best way of doing it is to scan the slides in a high quality slide scanner, but those are pretty expensive, probably in the thousands of dollars. I'm pretty sure that's the method they use if you get it done professionally. There are some contraptions that are supposed to illuminate the slide and you can attach a camera to it to take pictures, but I'm not too sure how well those work.