Can run ads and affiliates links on my website hosting on WordPress.com?

Yes, of course you can.

But there are some "rules" to follow when monetizing your website on WordPress.com.

It depends on the way you want to monetize your website.

Affiliate links and Sponsored posts

All plans can use affiliate links as long as you comply to their terms of use:

• You can’t post affiliate links to: gambling, get-rich-quick schemes, multi-level marketing programs, disreputable merchants, pornography, malware, or phishing-type scams
• You can’t create a website to solely drive traffic to expose affiliate links.

Ads networks

Only the Premium ($8/m) and Business ($25) plans allow using ads networks as follow:

• Premium plan works only with their own WordAds.
• Business plan supports using the following ads networks: Google AdSense, OpenX, Lijit, BuySellAds, and Vibrant Media.

As any explicit rule of any kind, trying to get around it will result of warnings or ultimately banning you as they see fit.

Make sure you check their monetization rules’ page.