There are various things you can do after defeating the Elite Four which vary from version to version. The following is what can be done, specific to each version released so far.
In Pokemon Red, Blue and Yellow, your main objective is to defeat the Elite Four. Thus, after you have done this, there are only so many options left in the game to complete. It is recommended that you complete the Pokedex by catching (or otherwise obtaining) all 151 Pokemon. Once this is done, there is nothing much more to do than build your team and take on the Elite Four once more.
In Pokemon Gold, Silver, and Crystal, you are able to do a few more things once you have become the region's champion. You can still enter the contests on the radio, catch bug Pokemon every Tuesday and Thursday in the National Park, breed Pokemon and fill the National Pokedex. Of course, there is also the option of battling Red in Silver Cave. Once you have defeated the Elite Four, Kanto becomes an area in which you can explore. The objective here would be to collect the 8 Kanto badges and face the elite Four once again. It is at this point that Silver Cave opens for you.
In Pokemon Ruby, Sapphire and Emerald, defeating the Elite Four opens up the Battle Tower and various options around Hoenn which allow you to obtain legendary Pokemon. Sky Pillar is unlocked, and Rayquaza awaits your capture. Latias and Latios are released into the wild in their respective versions. Of course, there are always the options of breeding Pokemon and even entering contests. Emerald is a special case in which there are various battle facilities open for you to master, even after you have defeated the Elite Four.
In Pokemon FireRed
and LeafGreen, access to a group of new islands is granted, giving you an opportunity to explore new regions and capture Pokemon more native to Johto. There is also the mini quest of fixing the trading port on One Island so you are able to trade Pokemon between FireRed, LeafGreen, Ruby, Sapphire and Emerald. There is also a mini games kiosk on one of the island which offers small games for you to play with friends. As with previous versions, you are also now able to capture various legendary Pokemon.
In Pokemon Diamond, Pearl and Platinum, there are still the options of breeding, contests and the Battle facilities. Of course, there is a new island containing the Fight, Survival and Resort areas. There are also more chances to capture legendary Pokemon (moreso than previous versions), resulting in a few mini plots after you defeat the Elite Four. The option of completing the National Pokedex - with a staggering 493 Pokemon to be captured - is always available.Answer
The bottom answer is completely wrong in every sense, first of all, you get Pal Park after beating the Elite Four and getting your Pokedex upgraded to National level. Also Darkrai is only obtainable via a Nintendo
Event in either Japan
In Pokemon Blue, you can go and get Mewtwo from Cerulean Cave. Once getting Mewtwo, you need to catch every Pokemon in the game to fully complete it. This involves trading from Red. You can also use the MissingNo hack to get better Pokemon to beat the Elite Four numerous times.
After you beat the Elite Four, in Yellow, go aboard the S.S. Anne to take you to another region.Answer
Well, after the Elite Four, if you have seen all 210 Pokemon then you can get your Pokedex upgraded by Professor Rowan. This gives you access to Pal Park, and Pokemon from other games. This also gives you access to more Pokemon Fossils underground, such as Kabuto, from the Kanto region....
Also, talk to Sailor Eldrich's kid, in the house right near the port in Canalave city, he should mention something about Darkrai, and darkness. Then talk to the Sailor's wife, then to Sailor Eldrich (the man who takes you to Iron Island..) The little boy would say soemthing mlike dark....dark..... becasue darkrai had just given him an nightmare. the the sailor will say go to full moon or new moon island and get this wing . when you get there, there will be cressilia and she will run away and drop this wing and you have to take it to the sailor.