The twitter API limits you to pulling the most recent 3200 tweets... so if you roll your own keep this in mind.

Also there a number of Twitter archive services out there that let you download a copy of your timeline. Remember that they too are limited to the 3200 by the API.

I happen to own/run one such service (http://tweetsaver.com). We'll get your most recent 3200 tweets from your timeline, plus all your mentions, DMs and favorites. We allow you to export these as a CSV file.

However, if all you want to do is download the tweets, my service is probably not the best option.