I'm interested in getting an Atari 8-bit (like I had 30 years ago), but have only LCD TVs (and computer monitors).
Can I hook this Atari to a flat screen TV, or do I need an analog CRT?
Most classic computers will work fine on a TV with proper composite inputs. You want to make sure your TV has aspect ratio selection as many simply horizontally stretch the 4:3 image to 16:9.
As for Atari's, it will depend on which model you have and what cabling you have. I've very successfully run Atari 800XL and 1200XL systems with LCD TVs using the proper composite cable like this one: http://www.ebay.com/itm/Color-Composite-Video-A-V-Monitor-Cable-DIN-to-RCA-for-Atari-800-XL-XE-6-New-/130888382784?hash=item1e798e3940:m:mEq5Xkccxwvlc7ClvaEIjWA
That is not my listing, I am only including it as reference.