By checking the logs on the machine the logs are on.

Besides, anyone who is tech savvy enough to mess with public key encryption is going to be using OTR anyway, making server side logs useless.

I'm using OTR, but only for conversations that are worth protecting. IMHO securing typical chat with friends (mostly consisting of funny/interesting link exchanges) is almost pointless.

But having the history is still useful ("remember that article I've sent you yesterday").

Not as pointless as most people intuitively think. What if the chat server you're using is compromised by a hacker trying to make a name for themselves and they publish all of the chat logs on bittorrent?

Some examples of comments in a private chat that might at first appear like they don't need encrypting, but might come back and bite you in the arse if they ever get published:

"God work is boring today. Need to update my CV/Resume"

"Bob was a bit of an idiot last night wasn't he"

"Thinking of skiving off work tomorrow."

"The wife has been nagging at me all afternoon. Fancy a pint later?"

Depending on how secure you want to be, the existence of encrypted/non-encrypted information reveals things as well. Someone could infer something by just knowing that you turned on OTR at a certain time.