Should I use it on different systems?
I've got a great password that no-one will be able to crack.
There's no easy answer to this one. Employ strong passwords where they are needed, and if that means using the same password on more than one system, then perhaps it's a risk worth taking.
You have to weigh up the value of the information your passwords are protecting and the trust you are prepared to place in the systems you are using. It's probably NOT a good idea to use the same password for your personal banking and for your favourite news site, and the same judgement needs to be repeated for all the services you make use of.
- (Some people keep an 'easy' password in reserve for all those online services that require you to choose a password before you can use them. This may be a reasonable approach in cases where you are not responsible for or concerned about the value of the information involved; of course, this does NOT apply to UCL computer systems!)