If you mean yoursite.wordpress.com than No you cannot add sdsense in wordpress. If you are talking about self hosted wordpress then yes you can add adsense. There are many plugins to do this job.
Yes i am totally agree with crazyblogger in Free word press blog adsense is not working you have to take domain and host on word press platform....
Yes u can add adsense in free wordpress blogs and blogger blogs like I'm using adsense in one my blog which is free, http://healthandfitnesstip.blogspot.com
If you want to make free blog with adsense then you can create in blogger.com because adsense program is not supported in free wordpress blog.
Of course you can add adsense on free blogs.. I have been using blogger and it allows me to put adsense..
You can not add adsense in free wordpress blog as free wordpress do not support to adsense. Even blogspot may help you.
You cannot use adsense in your free wordpress blog if you'll do this than your account can be blocked. For more information you can learn more from there http://en.support.wordpress.com/advertising/
if you using free word press like yoursite.wordpress.com then you can not use any plugin that is created for adsense ads, yes you can put your ad code manually ... and if you using paid domain on word press you can use any plugin for adsense.
if it suppots the adsense policies then there is a no problem with the adsense in wordpress blog. look at my .blogspot.com i am earning $2 daily frm it... search in google " hackbymak "
U cant use .wordpress.com blog for adsense... but u can use .blogspot.com for adsense if u want to...