Hehe, me and the missus have been playing this since release day and haven't run out of things to do yet, plenty more life left in it yet! I Played the Gamecube version for 2 years and never completed all the possible objectives.
Basically here is a sample of things you need to do to "complete" the game...
- Collect every fish going (rivers, ponds and sea) and give it to Blathers at the Museum so he can display it (all duplicates can be sold at Tom Nook's shop). It's worth getting a TV at some point as you can watch the weather forecast, if it's due to rain the next day it's worth fishing as you can catch some interesting stuff.
- Collect every insect, on tree's, in flowers, on the ground and flying in the air
- Look for cracks in the ground, dig to get fossils, hand these to Blathers and he will identify them and then build exhibits out of the pieces
- Tom Nook will get started with a mortgage for your house if he hasn't already, pay that off to get an extension (I'm on my 4th now I think, the latest cost over 600,000 bells!)
- You can also buy paintings every now and again for the museum, tidy up the town (get a nice even spread of tree's and flowers, pick up the weeds etc) to attract new residents, do up your house with some nice furnishings to imporve it's HRA rating
Also, as it's currently August there is a fireworks display every Saturday between 7pm and midnight, Tortimer will give you a sparkler or roman candle and you can enjoy the show!
There are many many more things you can do, that above is just the basics. It's certainly a game you either "get" or "don't get", me and the missus both have our own copies and both love it, so we visit each other etc. My most played game ever without a doubt.