I have heard that some say that you should limit the number of expression engine channels you use to about three regardless if you use the free or paid version. Has anyone else experience EE giving problems after you create more than three channels?
No idea where you heard that tip as it's simply not true.
I've worked on sites with upwards of 15 channels without issue.
Granted, the more channels you have the more fields you will have which may bloat the db but performance isn't really affected.
Maybe their point was give good thought to your channel/field setups to avoid duplication of content storage.
One of my websites currently has 26 channels. I needed to be able to use the same entry title for multiple entries so I made multiple channels to act as data containers. In this way, I can use channel entry tags or SQL queries to grab the channel quickly and do what I need to do with the data.
I also assign the same field group to several channels to keep the number of custom fields in use as low as possible. I believe that this is the more critical part as adding fields will quickly bloat your DB.
My average site has around 8 channels. Biggest site has 20.
Channels are generally analogous to database tables, if you're familiar with databases.
Best thing to do is familiarize yourself with channel preferences, categories, field groups, statuses, member access, and the channel:entries tag. After using those things in a few cases you'll get a better idea for good/bad use of channels.