I think always trash applies to cards that directly service the corps win condition. Bio-ethics, Zealous Judge, SanSan City Grid, Jeeves Model Bioroids are all cards that can do this. There's different situations where you're forced to trash a card for the sake of your chances at winning. For instance, if you can reliably keep clot on the board, SanSan City Grid becomes a neutered threat. If you can avoid damage and have no resources, Zealous Judge and Bio-ethics become less dangerous, assuming you can afford the protection. Jeeves Model Bioroids aren't always a must trash, but if a deck is playing Subliminal Messaging, Lateral Growth and Shipment from SanSan, you better trash that as soon as you can afford it.
In the case of cards like Caprice Nisei and Ash, these cards become important to trash to have a better shot at attacking your opponents servers. If you're playing Rumor Mill, they become less threatening. It all depends on what cards you have at the time, and have access to (in your deck).
Cards that have expensive costs are hard to trash immediately unless you are playing Whizzard or have Scrubbers out, or your opponent has bad publicity. These can create scoring windows for your opponent when you dip to a low credit amount.
You generally want to trash cards like Adonis Campaign if they aren't protected, or any economy asset that is unprotected for that matter. This is obviously different if it's, say, a PAD Campaign or Marked Accounts, and you're at such low credits you would waste your whole next turn clicking for credits. If you're playing a denial deck, you would want to hunt down revert economy cards with extreme prejudice, but sometimes you can't find your economy and you have to make a decision as to whether you want to say, build your board state or pressure the opponent for accesses.
If you notice that the Corp is able to do things they otherwise would not without a certain card, trash that card when you see it, don't let the corp gain use out of it. You'll get used to these situations eventually, people will mention combos of cards that are generally played in specific factions, and you'll know to look out for these cards during your random accesses during the game.