MultiBit Classic has been an excellent workhorse over the years (It has it's fourth birthday next week !) and we will do periodic network and safety updates as necessary to keep it operational. All the good stuff will be going into MultiBit HD though.
Keeping your bitcoins secure basically boils down to keeping your private keys safe and intact.
Because MultiBit Classic has random private keys there is no getting round keeping backups (we recommend at least two copies of both the wallets and private key exports stored off your main machine).
A useful way to reassure yourself that your backup strategy is effective is to try it out on another computer.
Imagine your laptop/ main computer has died or is stolen and check you can recover your bitcoins on the second computer.
If your backup strategy works well then that shows that there is no
need to change your Bitcoin wallet.
However we think deterministic wallets are better all round which is why we created MultiBit HD.
(Also Electrum, Armory, Mycelium, Schildbach Bitcoin Wallet and many others now use deterministic wallets.)
Hardware wallets are better again which is why we have added Trezor support to MultiBit HD.
If you have a birthday coming up why not treat yourself to a Trezor from
https://buytrezor.com and try it out ?
It is compatible with various wallets and means your private keys do not touch your main computer.
You can try it out with a small amount of bitcoin (perhaps over several months) before committing larger amounts of bitcoin to it.