Yes, you can use an active DVI - D to analog RGB converter and, if the card has no analog capability, that is the only way to connect to an analog only monitor.
If you are using your PC to display modern encrypted content then make sure you get a converter that has this capability or nothing will play.
In terms of display quality, I find very little difference caused by the type of connection (analog or digital) if quality cables are used. In general, modern fixed pixel displays look best when fed their native resolution.
Older CRT monitors can switch resolutions but they still have a phosphor pitch that acts as the equivalent of a native res so, they also look best when fed something close to their sweet spot res.
I keep analog CRT arcade monitors for vintage gaming (240p, 384p and 480p) as old arcade games look horrible on modern displays. For everything else, it looks best on an HD flatscreen.
So.... unless you are looking to play vintage games.... it's time to upgrade to a digital monitor.