I recently got myself an i9003, a Galaxy S variant. This is my first android device and so it took me some time to figure out what apps to download and what to avoid.
So here's a list of my favourite apps.
1. Poweramp - Without a doubt the most functional and versatile music player on the android market. Plays any audio file you throw at it and has exceptional library/organizational abilities. A must have app for around $4.
2. Read It Later - This is a special app. What this does is that it gives you a reformatted version of web pages so that's it's easier for you to read articles. This is much like the article view on Kindle 3. Although not free, this is very much worth what the guys are charging for the app. Also future developments and browser integration only justifies that price tag.
3. Doggcatcher - One of the more expensive softwares out there. This $6 app is a podcast manager like no other. With integrated Google listen/reader syncing ability, the ability to auto download content, this one app is a must have for any podcast enthusiast. There are of course other free and paid podcast apps in the market, but none are nearly as efficient and customizable.
4. CacheMate - This thing is only available for users who have rooted their phones. Outstandingly simple to use this extremely cheap app lets you clean cache memory from each and every app saving you precious disk space.
5. Juice Defender (Ultimate) - Juice Defender is actually quite a popular app. It lets you save up on and reduce data usage on your mobile device thereby substantially increasing battery life. Although it is difficult to say the extent to which this battery saving ability works, its pretty evident that it does take visible measures to reduce data loss. I would recommended the ultimate version as its more useful and cheaper in the long run.