TeamViewer is completely free for personal use.
It's a bit pricey for business use, but that doesn't prevent TeamViewer from earning our Editors' Choice award for remote access software. It also works across platforms and is free for noncommercial use. TeamViewer does both of these things extremely well, in addition to offering some of the smoothest remote controls on the market.
And if you're primarily interested in accessing specific machines, you want software you can sign into securely and leave running in the background. If you're providing remote access support, it's crucial that the software is easy to download and set up, because the person on the other end isn't necessarily tech savvy.