The BBC News website has been speaking to Zimbabweans who have left the country in recent years about their reasons and the risks they took.
Last week the International Organisation for Migration launched a "Safe Journey" campaign in Zimbabwe, with help from some of the country's best-known musicians, to make would-be migrants aware of the dangers involved.
Constantine Kureva Mkinya, 44, explained how Zimbabwe's secret police caused him and his two small children to make America their home.
Life in the US became easier for Constantine when he realised that his children were settling in so well
I came to the US in April 2003 after consistent and persistent harassment from Zimbabwe's secret police, the Central Intelligence Organisation (CIO), after I refused to accept a position as a High Court Judge.
I had had a successful private law firm in the capital city, Harare however after going through a dreadful divorce in 2002 I was forced to reconsider my priorities.
I had been given custody of my two young children and felt that the long and unpredictable working hours required of me were no longer viable.
A friend of mine encouraged me to apply for a vacant judge's position - where the hours would be very child friendly.
The recruitment process moved along positively - my CV and personal circumstances had all been vetted and rendered clean by the CIO.
Controversy and corruption
In late 2002 I was called to finalise all the details of my imminent appointment.
That was when I realised that the position was mired in controversy and corruption.
I was told in no uncertain terms that I could not exercise any professional independence as a judge.
And if I took the appropriate action expected of me, by the government, I would duly be rewarded beyond my imagination.
Naturally, I turned down the offer.
I did not want to practise corruption for a living.
I said that because of my ethics and conscience I would not let someone walk scot-free. Nor would I lock someone up if they were innocent.
I was informed that my views were in conflict with those of the government and very embarrassing for the president so the position was no longer available.
That afternoon the state controlled media reported that I had lied to the nation and there was no truth in the claims that I had been appointed as a High Court judge.
Constantine's children were very frightened of the police
I then approached the independent Daily News newspaper to clear my name. But this made things worse because my story made a lot of sense.
I started receiving threatening telephone calls and it was obvious that I was being followed. My phone calls were being monitored. The country's secret police broke into my office, ransacking it.
My children became very aware of a frightening police presence.
I was very lucky in that one of the guys looking for me from the CIO was very helpful. He gave me titbits on how they were looking for me and so I changed the patterns that I had become well-known for and stayed one step ahead.
Over the years I had helped several police, Army officers and a few people that worked in the CIO with legal problems. Word had got around that I was decent to deal with and this one gentleman kindly returned the goodwill.
With help from friends, I took an overnight bus to South Africa with my children late one Friday night in March 2003.
From there we flew to Dallas in the US.
A human rights initiative helped me apply for asylum and the system worked like clockwork. Because I was going through the court process I couldn't work during my first year but the US government's Housing Crisis Center provided for us.
Constantine now lives in Phoenix
It has been difficult and very humbling.
In Zimbabwe I had more money than I knew what to do with.
It was difficult coming to terms with having to get someone to sign a voucher so that I could have a new pair of socks. It made me crazy and I almost lost my mind.
I applied for more than 600 legal jobs but did not get one. Not even as a paralegal secretary.
Things changed when I realised that my children were settling in so well.
I took my kids to the police station near us one day. I wanted their fear of the police to disappear and for them to be comfortable calling them for help if need be.
It was a very good public relations affair - I explained to the officers about where we had come from and what had happened and why the children were so frightened. They took us round the station.
Constantine's children are not frightened of police anymore
It showed my kids that things were different now.
After having to work on any job that I could lay my hands on I am now a case manager looking after mentally ill people and in six months time they have said I can transfer to the legal side.
We currently live in Phoenix, Arizona and soon I begin studying part-time to convert my law degree.
I am one of the lucky ones and I am now on my way.
There's nothing compared to being back at home but for now it is the last place I could think of being.
I'm very happy with my life here in America.