My list of absolute essential android apps to have:
Most of these have tablet optimized UI too (The same install looks different on phone/tablet)
Evernote – The ultimate super notepad, which you carry every where. Its available on multiple platforms (PC, Mac, Android, iOS, WP7 etc) and it keeps everything in sync via cloud. Its free.
Due Today – Its the best task management(day organizer) I found on android market. It too syncs ur tasks on cloud so that u can see/edit em anywhere, device independent. The sync in done via toodledo.com(account creation required, its free). The ad supported version of Due Today is free n ad free is around 150 Rs.
Tango – As skype ppl have been very lazy in implementing video calling on all android phones/tablets, this is an alternative. It recently released a PC version too(with the most functionally useless UI I have ever seen). Free.
Dolphin browser – An alternative to the default browser. They recently released a tablet optimized version, very well done.
Ez pdf reader – An excellent pdf reader with page turn animation. The ad free version is less than 100 Rs.
Repligo reader – Same as above, but without page turn animations n also its more expensive.
Saavn – Great for streaming bollywood songs. Ad supported, free.
Opera mini – Another alternative to the default browser. If you have low bandwidth connection, this will help you out. It has the fastest page load times.
Pulse – An amazing news aggregator app. It will download news/stories from your selected websites at a single place. Free.
News 360 – Same as above but a totally differnt approach to presentation. It has interesting widgets too. Free.
Google sky maps – An interesting idea.
Latitudes – If you wanna let your friends know where you are.
Google goggles – Augmented reality + Google search. Microsoft recently releases bing vision in response to this. (Note bing vision is integrated into WP7 mango devices and as of yet not available on android.)