My son is 4.5. He's still in a toddler bed. He's about to outgrow it though! We told him a while back when he was night-time potty training that as soon as he stopped wetting his bed, his reward would be a Big Boy Bed with Big Boy Sheets. He's been dry now at night for a while, but we still haven't gotten him the bed. We have a friend building it. But we have shopped for sheets and have bought the comforter. We are waiting for the bed to be made so we can go buy the mattress.
So to answer your question in short: Age necessary - when our son started getting taller/longer did we start considering it. Then there was the talk of not wanting pee all over a new mattress. So now that he's long and dry at night, NOW is when we are getting the twin.
@What Dawn and others said about picking sheets/bedding. My husband did not want some giant cartoon picture as the bedspread (Spiderman, etc). He wanted the room to look nice and match with decor/paint. So we told our son he could pick out any sheets he wanted, but Dad got to pick the comforter. All is good. I mean, sure the sheets and comforter might not match, but as long as the bed is made, nobody will notice. Pottery Barn had very cute plaid comforters. Target does too - with lots of colors in them so it could match almost any room.