I check email often and view whatever message(s) I might find there. Of course, with my low-volume email life these days, I frequently feel like the lonely Maytag repairman. (Does that analogy betray my age?
)
As far as texts, my cell phone is only for important calls, not casual conversation, so if any of my contacts send a text, I view it immediately as well. And a few contacts' emails are forwarded to my phone because of their importance.
So, generally, yes, I check messages asap.