Sacrifice to force king to move

Is it viable to sacrifice a minor piece to force the king to move and prevent a future castling?

A pawn for castling often provides enough compensation. A piece for one or two pawns without attacking prospects is usually not enough, eg 1. d4 Nf6 2. g4 Nxg4 3. d4 Nxf2 (or 3... d6 4. Be2 Nxf2) is better for White and 1. e4 e5 2. Nf3 Nf6 3. Nxe5 d6 4. Nxf7 never enjoyed a great reputation.

Usually you need two pawns and an attack to be worth sacrificing a minor piece.  However, the way to really get a sense for what sacrifices work is to try a few on speculation.

Sacrifices on f2/f7 during the opening can sometimes be worthwhile, even if you net only one pawn, but usually you will need to be able to follow up the Kxf2/Kxf7 with another check immediately.  It's usually best to complete your development first, though.

I sometimes trade queens by moving my queen straight up the d file to force the opponent's king to move to capture it, though I'm considering encouraging a queen trade where my opponent takes my queen first, but my queen is situated where the piece that captures the opponent's queen gets some development out of it.

In the Fried Liver attack, you get an excellent attack by sacrificing your knight:

yes, I love to play that

Theres also something known as the positional exchange sacrifice where you trade down an exchange to get a positional advantage