"I remember those years well."
I looked up "ricordarsi" because I had a nagging feeling something was missing> And yes: "mi ricordo bene DI quegli anni." I generally use the reflexive form with the preposition "di". As Italian is not my native language it was a choice I made, because it is easier to remember one situation instead of two. "ricordare" is all right too.
I translated this as "Mi ricordo bene quegli anni". I did a Google search on "mi ricordo" and got 6,450,000 hits, including popular songs, book titles, etc. Can someone please explain (a) why my answer is wrong and (b) when are the reflexive forms of verbs like "ricordarsi" to be used. (In answering (b) you might want to keep in mind this quotation from Maiden & Robustelli's A Reference Grammar of Modern Italian (Chapter 6): "A few intransitive verbs can be used with or without the reflexive clitic: ammuffirsi/ammuffire 'go mouldy', approfittarsi/approfittare 'take advantage of,’ ricordare/ricordarsi 'recall', 'remember'"