It very much depend on the game, and my idea for it. I usually give the premades a make-over and just like having them around and make my own head canon about them. Most often they are just background, sometimes friends, but it does happen that I play with them too.
In one save I started out as Johnny Zest, he briefly dated Dana Caliente, but ending up marrying an original sim and moved to Sulani and broke it up with Dina when his wife to be found out he was flirting and almost threw him out. To be fair I've never seen such a realistic reaction before, and she didn't even have the jealous streak! Johnny literary had to beg to make her forgive him. It was such fun to play. He lived to a ripe old age and had two adorable children.
I've also played the Pleasants, though I quickly became quite fond of Angela, struggling to keep her wild sister in check. She found a random townie to marry who came over randomly because he heard she'd just got a dog. They ended up having 5 kids and moving to Brindleton. I got quite attached to their "little" family.
In my present save Julia Ward is a close friend of one of my sim, and a sort of mentor of her career introducing her to all the right people. The Goths are related by marriage to another one of my sims (although this is technically not the premade Goths, as they have not been born yet. Mortimer's grandfather Victor is set to age up to a teenager fairly soon.)