If you are using a stock WordPress installation, take a look at your robots.txt file and it will most probably say something like:
The problem with this is that there are many bots which will hit you very hard if you don’t specifically block them. Here is a better robots.txt file:
Feel free to fork and create better versions.
Just keep in mind that there are still a lot of other bad/useless bots out there which will consume your resources, but many of them do not respect robots.txt. You will have to block their IPs in your .htaccess (or other similar conf files depending on your server).