Very often I see the ek- being used as a complete synonym of "start doing something". But it feels wrong. PIV defines this prefix as
Pref. signifanta, ke la procezo komenciĝas subite, je preciza momento
and proceeds to give examples like ekdormi (fall asleep), ekvidi (to catch sight), ekbruligi (set fire), eksidi (sit down) etc. These are different – instantaneous – actions as opposed to just "start sleeping", "start seeing", "cause to start burning", "start sitting".
Certainly, in other examples this may be indistinguishable or almost so, like ekparoli, but this is no justification to pushing the "start -ing" sense everywhere.
A particular example I have in mind is Mi eklernis Esperanton pasintjare. This feels like a misuse because eklerni refers, according to the above definition, to the "preciza momento" the speaker first opened the book, while this is hardly what they want to say. If the intended meaning is the whole set of processes of making the decision to learn, choosing suitable resources, finishing the first lesson, is this still a ĝusta formulation? Shouldn't it be rather replaced by Mi komencis lerni?