It depends on what kind of trust you mean.
A Scorpio will take your secret to the grave.
A Cancer who says they love you forever will love you forever, beyond the grave. They will fight for you no matter what.
A Taurus will never gossip about you, and will always kindly assist you when you need help. They also really love you if they finally say it.
A Capricorn may covet the same job as you, but whatever else passed between you is private.
Beyond that, I've thought about this, and I'm going with Scorpio.
A Scorpio will keep your secrets, testify for you in court whether you did the crime or not, and love you madly. They win, hands down.
Thanks for a great question that forced me to think! Signs not mentioned aren't big on trust issues. I'm considering the factor that many signs talk too much. For instance, a Virgo friend will always give sensible advice and be there for you. But they talk a lot, and will tell the whole world everything you said. Aries only care about themselves. Geminis lie. Leos can't be bothered. Libras either. Sag is truthful, but again, will tell the world your problems. Aquarius is too detached. Pisces is sympathetic, but wrapped up in dreams.
So earth and water signs are most trustworthy. But get one good Scorpio friend in your life, and you have it made. They would move mountains for you.