Ex-catholic here!! Strangely enough, when I was a Catholic, I didn't have any particular reason for wearing one other than it was a symbol of my faith.
But now I undertand that the cross for Christians is a sign of Christ's victory over death, as well as a reminder of his suffering for the wearer. You'll find differing viewpoints between the denominations but they're mostly based around these two ideas.
Often RC's will wear a crucifix (or have one in their home), these have an image of the crucified Christ on them, whereas protestants will reject these because of the idolatry and because their focus is more on the empty cross - the nearest symbolism you can get to Christ's victory over death and the empty tomb. The more 'liberal' Catholics sometimes take the middle road and have an image of the risen and glorified Christ superimposed on a cross.

I do think that there is some idolatry towards crucifixes in the RC church, it was one of the first things which began to rile me when I was in my fading stage. On Good Friday, they had the 'veneration of the cross' where everyone would go and kiss the feet of the figure of Christ on a crucifix. I found I just couldn't do that, I saw it as blatant idolatry, even though its 'only' meant to be a symbolic gesture towards the real Christ. I just couldn't get my head around it at all.
Some Catholics are also very superstitious about the crucifix giving you protection from evil, often why they are hung in houses. The one we had in our house used to keep me on the straight and narrow because it reminded me that Jesus is watching me...
...and that I'd go to hell for eternity if I sinned and died before I went to confession - better not sin then
I never had a heavenly hope as a devout Catholic - I never thought I'd get past purgatory!
On the face of it, writing this post makes me realise what my RC practice was based on - a fear of death and hell, although I can't say that is the same for all RC's!
Ah sweet freedom