Yes. It won't be free, but consider the cost of getting some other TV and all the convenience and nice picture it will buy you and I say it will be totally worth it.
The video technology is quite different so you need a device that will convert (not just adapt but actually do some conversions) a video signal to vga or dvi (depending on whether your lcd is vga or dvi or both). If you are doing DVI then be wary of several versions DVI-D or DVI-A or something like that ...
^^ Is probably the cheapest way to do it. I use a vdigi transcoder that allows me to connect any component cables and hi def signal(select PS2 games and most Wii games) and I run it to my monitor that way. But it was $60 after some discount. That wii specific one is fairly cheap compared to other options.
Take heed, doing this will give you a jaggy picture as most monitors are 1280x1024 (for a 4:3 ratio) whereas the Wii outputs in 640x480 or 852x480 (widescreen).