In most cases, you can record your keyboards using the line in of your computer. This can be perfectly adequate for most, even for those with multiple keyboard/modules although it will require a lot of connecting and disconnecting of cables. (I used to do it when I had more keyboards and modules than soundcard inputs.)
Vocals are another matter since you will need a good mic and preamp. dequi09 made a good case for using a mixer, which again is perfectly adequate for most cases (demo recordings, for ex.), but if you want studio quality vocals, a studio really is the best place to record vocals. I did that with early recordings, recording my midi setup then mixing a raw track to sing over to. I recorded vocals in another studio which had better mics (AKG 414 in one and U87 in another), got the raw tracks of the vocals which I transferred to my pc for final mixdown.