My first introduction to the world of anime came in the 80's when Dragon Ball was shown on Dutch television. Growing up in Germany you got a lot of anime shows on European Networks, and the likes of Transformers, Gatchaman (Battle of the Planets in it's butchered US/UK state) became staples of my childhood.
However moving to the UK lost me my anime for a good long while as the medium had little to zero presence in this country, and even now remains relatively inaccessable. Fortunately in mid 90's UK sattelite channels such Bravo started showing late night Manga lable movies and OVA's such as Akira, GITS and Street Fighter. I was immediately connected back into the unique style, unflinching subject matters and dense plotting that drew me to anime in the first place. At this point shows like NGE and DBZ started becoming available on high streets and channels like Cartoon Network and Fox Kids started showing shows like Gundam.
Now, thanks to the internet, it's possible to get hold of anime easily and keep up to date with new stuff!