If you are just going to hook up component video output to your monitor, then the VDigi Enhanced VD-Z3 will work great. It can be used with any component video output, so it is not limited to just being used with an Xbox. Read
TeamXbox's VDigi Enhanced VD-Z3 review for some detailed info about this unit.
If you want a more complete solution, then I would suggest using a
Pelican System Selector Pro and a
ViewSonic NextVision N6. I have a small bedroom with my computer and 21" NEC CRT monitor in it, and I use this combo of equipment to have my 3 consoles (Xbox, PS2, & Gamecube; all with component outputs), region-free progressive scan DVD player (with component output), progressive scan DVD recorder (also with component output), Super VHS VCR (s-video output), and finally Dreamcast (again, s-video output; I have the VGA box for this, but not all games can support VGA output, so that is why it is connected by s-video as well) attached and viewable. The progressive scan output on the screen is incredible, especially close up. You'd swear that you were looking at a HiRes video or a computer game. Normal output (like from the TV tuner or s-video) has to be line-doubled, but it looks better than normal TV whether you sit close to the screen or far away. There are no artifacts during fast motions and no pixelation. The NextVision N6 even supports up to 1280x1024 resolution, so you should be able to use this with your LCD monitor at it's native resolution.
Now for the downsides of my combo. First is price, it's going to cost you about $250 (includes shipping). I did some price finding, and you can get the NextVision N6 from
Ebuyer for $165.95 (includes shipping, to my state at least

might be a little more or less for you) and the silver-colored System Selector Pro from
Video Game Deals for $80.98 (includes flat-rate shipping) or the black-colored System Selector Pro from
eCost for $72.94 (includes free ground shipping and eCost's usual $4.95 processing fee). I used these three companies because they were the lowest prices out of all the listings in the price searches from companies I have purchased from before and had good experiences. You can definitely find them for less online, but as always, buyer beware. Also, this does not include B&M stores which may have sales on this equipment. Second is the connection to the monitor, it is VGA only, not DVI. But then again, I don't know of any computer monitors that are DVI only, so this is really not an issue. Last downside would be the number of certain inputs on the System Selector Pro. There are only 3 optical digital audio inputs, NO coaxial digital audio inputs, and only 3 network inputs. The number of optical digital audio inputs is not an issue for me now, but when the next gen consoles come out, I'm going to have come up with a solution as I will need more inputs. The network ports are switched, in other words, if you turn off the System Selector Pro or change to another piece of equipment, the port is turned off. Not a good thing if you want to have multiple pieces of equipment connected to the internet at the same time, such as your Xbox and Tivo. So another piece of equipment you might need to buy is a network hub. Network hubs are relatively cheap now, about $20 for a 5-port version. Other than these mentioned problems, which are minor at worst, I am very happy with my setup.