About 1 year ago, I bought an An Eizo L675 (cost about $3000 ). Its an 18" LCD with both analog and DVI inputs, and is still among the best flat panels available in terms of image quality and response time. The analog quality is truly excellent, but when switching between analog and DVI, its very obvious that DVI is still a massive improvement in picture quality.
The big downside, especially for gamers, is that because of a totally stupid limitation of the DVI standard, DVI only supports a maximum refresh rate of 60Hz!!! I really couldn't beleive how [-peep-] short-sighted the designers of DVI had been when I realised this.
Another point for gamers is that even an average CRT still has a far quicker pixel response time than the best LCD. Perhaps because of this, they thought that DVI support for more than 60Hz would be redundant.
I've found by experience whilst playing UT, even though it looks pin-sharp and dead sexy, you just can't be seriously competetive with the DVI limitation of 60Hz. Since "upgrading" from a CRT to flat panel/DVI, I've had to get used to regularly getting fragged before I've even seen the other guy.
The choice comes down to this: If you want a crystal sharp beautiful image (great for work and watching DVD) use DVI without a doubt. But... if you need a good gaming machine (i.e. higher than 60Hz framerate) then you're almost certainly better off using the analog signal, or even better sticking with a good CRT.
Another downside with DVI: You still need both analog and digital signals to your monitor anyway because most DVI-enabled video cards only have either DVI or analog output enabled, not both at the same time. They power up with the analog output enabled by default, then only switch over to a digital output when the Windows display driver tells the video card to. This means you only get DVI quality under windows.
To complicate matters further, you need to take extra care when buying a DVI-enabled video card to make sure that its DVI connector carries both analog and digital signals (as it should according to the DVI standard).
Most cards (my Hercules Geforce 3 for example) stupidly don't have the analog output also connected to the analog signal pins on the DVI connector. I therefore have to have 2 monitor leads connected to my monitor. One in order to be able to see both the PC bootup and bios screens (from the analog signal on the 15 pin D connector) and the other from the DVI connector to be able to see Windows. Thankfully my monitor has 2 input channels that automatically sense and switch. Most monitors only provide one input though...
All this makes me wonder what the designers were thinking...