So, I have 2-3 php scripts that I run as crons calling them using wget: /usr/bin/wget -o /dev/null
These files (cronrss.php) are getting copied in the directory every time the cron runs, every new file having a new number (/home/example/cronrss.php1, ...cronrss.php2 etc)
So, what could be the reason for this strange behaviour?
I'm not very good with this but I guess the cronjobs are configured properly. They're running once per day, every middle of the night, at minute 0, then 5, then 10 etc.

wget is intended to download remote files via the command line, so what you're explaining is the expected behavior. The -o option is for logging output, where the -O option is for file output. If you're just wanting to download a file but throw all data away then use something like this:

wget -o /dev/null -O /dev/null - >> /dev/null 2>&1

I'm not sure I fully understood your instructions. I just want to run a simple php script. It works when opened in browser, it is removing some old database tables; is working as a cron, too, but I don't want the file copied all the time.
I used the -o /dev/null because I've read it should stop email being sent to owner, therefore save a little resources on the server's side. Am I wrong?
Thanks for trying to help.

Try swapping out your cron line with the one I provided and see if that does the trick

Well, until you try you don't know :)
Your cron line work exactly like I wanted to, silently; no files are being copied now and no emails are being sent to user.
Thank you very much, Sknake!