Ad-aware is not a firewall like ZoneAlarm or a virus scanner like McAfee, so it will act differently.Each time you run Ad-aware you will see new objects.Install SpyBot and you will most likely get very similar results.
Adaware (and spybot) only detect what is present on your pc ---they do not stop things being put there as you surf the web (spybot can innoculate against a number of these).So if you use them to remove adware/spyware,it wont stop them from coming back when you next visit the internet.
Most of what you are getting is most probably Spyware. Ad-aware and Spybot will get rid of them, but what you need most is to stop them getting on your machine in the first place. I would suggest and recommend "Spyware Blaster" which you can get from here. click here
Most things showing up in ad-aware or spybot , have been downloaded within web pages/sites , as you have requested a particular page your Firewall has allowed it , if you block your web browser then no surfing , ad-aware etc are not Anti-virus programs and therefore do not detect viruses.
These objects , could be anything from cookies (as others have pointed out) ActiveX , BHO`s , Dialers , registry changes etc , embedded in web pages , using exploits that havent been patched .
You need to keep your Operating System up to date , along with your Web Browser , firewall and Anti-Virus alike , they all perform different tasks .
As pointed out above , post details of anything your unsure about , and people will try to explain them to you , not all things that show up in Ad-Aware and SpyBot are bad , you need to read and check any new objects , and deal with them accordingly , some other programs can restrict browser options from being changed , these could be shown up as bad , yet they are not .
Most objects are just cookies. They do not normally do much harm. If you got to internet options under tools on IE and delete files and delete cookies, then you run adaware, you will not find them anymore.