It's possible and easiest to do if the news site provides RSS feeds as they are much easier to parse than HTML.
If xmlHttpRequest (aka AJAX) was used, you would probably get browser security warnings because your site is running scripts which try to load data from other sites (domains). There are ways to get around this using other techniques but you are probably better off using PHP for this. Then your news aggregation would still work if the user has turned off JavaScript, and you get better control of how and when the news is aggregated, caching etc.
I've been working a lot with the CMS/Drupal lately, there is an optional core module (Aggregator) which does all this for you and there are contributed modules which do the same thing but also allow these aggregations to be automatically 'transformed' into other data forms such as content nodes (ie pages on your site).