Openings that cause closed positions/open positions

Are there any openings that tend to cause closed positions (so I can use) or tend to cause open positions (so I can avoid)?

I don't know any.

Well, how splendid.

french, caro kann, king's indian defense are likely to lead to closed positions. If someone really wants an open game it will be hard to stop them getting one though.

Why do you want to avoid open positions? To master strategy, you will have to master tactics. And tactics flows from open positions. But back to your question:

1. e4 generally gives open positions. White can indeed force opening of files with gambits like kings gambit. Here is a few variations:

Closed positions often arise from d4, but a few from e4 openings:

The Czech Benoni is a quintessential closed position. 1. d4 Nf6 2. c4 c5 3. d5 e5 4. Nc3 d6 5. e5. 

The mad, bad and dangerous to know Polugayevesky Najdorf Sicilian 1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 a6 6. Bg5 e6 7. f4 b5!? 8. e5 dxe5 9. fxe5 Qc7 10. exf6 Qe5+ 11. Be2 Qxg5 leaves only the e6 pawn in the middle.

Both of these openings require cooperation from both sides. The Polugayevesky is rather long, and White can try to transpose into the Symmetrical English with 3. Nf3 against the Czech Benoni. The move order 1. d4 Nf6 2. Nf3 c5 3. d5 is awkward because e5 is under control and White can avoid playing c4 at any rate.