My personal campaign world is rife with demonic and diabolic machinations, but the party almost always deals with minions and "sub-bosses". The Big Bads never materialize on the material plane itself, but occasionally make an appearance when the heroes get powerful enough to take the fight to the Lower Planes.
I never used the fiendish lords in 1e... other than Lolth's appearance at the end of the classic GDQ series, Orcus in the abominable H1-4 "Bloodstone" series, and Zuggtmoy in T1-4. In each case, they were little more than "final bosses" to be slain (...what can I say? I was young...).
In 2e, I had a Planescape party participate (unwillingly) in a grand hunt by Mammon, Lord of the Third. However, I didn't need stats for him. If an archdevil catches up with a group of 9th level characters, they die. End of story. Similarly, the party also encountered Dispater (as part of the Fires of Dis module), Gra'zt (For Duty and Deity module), Pazuzu (...tried to trick the party into saying his name three times and summoning him in material form to the Prime Plane) and a couple of others. None of these were combat encounters.
I've used Orcus again in 3e, this time in a module of my own design. Demogorgon, Yeenoghu and Graz'zt also made appearances, but the PCs never fought them. The party was Epic level (about 24th level on average), and it was the culmination of a massive Abyssal double-cross.
I haven't used any of the archfiends in 4e yet, simply because none of our parties have yet reached Epic level. However, I have every intention of doing so at some stage.