Hi...I am about to build a project that records weather details for a period of 10-12 months without any reset or power down.While reading through the forums,i read few members reporting problems when running arduino continuously over a long period.

I am using atmega328P with duemilanove bootloader@16MHZ

Please advice me if any measures to be taken....Thanks in advance.

Well, lots of possible problem areas. What is your power source, and how reliable is it? How are you recording the information? How successible to lightening strikes?, How important is this data?
Do you need a low power (sleep) mode?

As long as your power source is reliable and there are no hardware or software bugs/defects, it should be fine.

Almost 20 years ago, I built a vehicle alarm (using a different microprocessor). It runs 24/7 even when not armed. It's still running... The only time it's shut-down & reset is when the car battery dies every several-years.

Unless you're providing it with a UPS I suggest you design it to cope with being switched off and restarted arbitrarily. That means that any data or state you need to keep long term should be stored in some non-volatile way, and you should design the use of non-volatile stores to be tolerant of being switched off mid-write.

Also ensure you design you solution to be robust - I suggest you enable brownout detection, avoid use of dynamic memory and keep your memory use simple.

Might be worth taking a look at the watchdog timer too.