Weather Underground offers free current conditions boxes, with no registration required. Their site looks a little clunky compared to AccuWeather, the Weather Guys, or Intellicast, but their "sticker" for your website looks pretty good. The code they provide is a comparative lengthy table--which leaves you some possiblities in rearranging it if you are so inclined.
The Weather Channel
Intellicast offers a nice current conditions box, and a number of other free products. They now require registration. Their code is in the form of an inline frame. When I obtained a current conditions box, the code read HEIGHT="204" WIDTH="304" but the actual size of the box is 172x244, so you might need to adjust these parameters.
Intellicast offers current US national and regional current radar maps in a thumbnail image-- but it is very small (140x90), and the link cannot be set to open in a new window.
Time and Weather
Time and Weather, from OnYourSite.com, supplies ticker which displays the current time and weather conditions in any of over 125 world nations. They used to supply a java applet, but now they provide an insert that requires that you have PHP running on your server, which, of course, almost all web hosts do.