Vince McMahon seems to hate competition. However, history has shown that having strong competition makes the industry stronger. The WWE, even though it is still the most popular brand in the industry, is not as strong as it could be and is certainly not as strong as it has been. Although the competition with TNA has helped to some extent TNA is certainly no WCW. The way things are currently going in TNA I can not see them ever having all that much of an affect on the way things are run in the WWE. We can all hope that ROH or one of the other up and coming promotions will be able to burst onto the stage and give the WWE a run for its money and improve the industry as a whole. But let's face it the WWE has the legacy, the fan loyalty and, most importantly, the money. Unless there is another Ted Turner out there with the capital and the television stations to really push a promotion it doesn't look too good for the competition.
In my opinion much of the downhill slide that the WWE has been taking started not with the death of WCW but at the end of the Invasion storyline. The end of the Monday Night Wars and the death of WCW itself didn't have as much of an immediate impact on the WWE as it could have mainly because they kept a pseudo-rivalry going with the storyline Invasion by WCW and ECW. WWE has already brought a watered down version of ECW back to life for a while, which shows that they may be open to the idea of bringing competition back to life if it helps them in the long run. Why not use this idea full force?
Here is my idea on how they could bring some competitive spirit back to the company: actual competition between shows. This basically takes the pretty lame "rivalry" already in the WWE storyline and pushes it to the next level though it would require bringing ECW back to life yet again and rebranding Smackdown as WCW Friday Nitro. It would also require moving all the Divas to one show, resurrecting the Cruiserweight division and possibly bringing in some more little people. At first this would mean spending more money but I feel that it would start bringing in quite a few more fans and their money fairly quickly.
All of these shows would remain under the ownership and oversight of WWE Corporate. However, each show would have its own wrestlers, commentators, creative staff, etc. Ratings for each show would determine what percentage of the total budget that show would get. I.e. if one show got 50% of the total ratings for the quarter that show would get 50% of the quarterly budget to use for bonuses and to hire wrestlers, commentators, writers, etc. from the other two shows and from other promotions. This would mean that each show was competing against the other two without actually drawing fans away from the other two since they would not be on at the same time. The bonuses would be for ideas and actions that drew ratings the previous quarter and would thus create a competition which could bring about new storylines, better moves, better gimmicks, etc. Also, each show would host four pay-per-views per year using only their commentators but, likely, having wrestlers from all three shows competing on it. Also, Corporate could host a few pay-per-views per year where wrestlers from all shows compete.

Here is an example of the new set-up:

WWE Monday Night Raw
Rules: Current
Titles:

Tier 1: WWE Championship
Tier 2: Intercontinental Championship
Tier 3: European Championship
Tag Team: WWE Tag Team Championship
Novelty: Divas Championship

Possible PPVs: Wrestlemania, Royal Rumble, SummerSlam and Survivor Series

Right now women's wrestling in the WWE is pretty much a joke. Most of that has to do with the WWE's obsession with hiring hot models as wrestlers instead of getting women with real talent. Some of it is also due to the fact that there are not really enough Divas to have them split up between two shows. If the WWE wants to keep going with the Diva's Championship they should get some real women wrestlers like they were apparently trying to start doing with the signing of Awesome Kong/Karma but at the very least they could increase competition for the belt by having them all on one show.

WCW Friday Nitro
Rules: Current Smackdown rules
Titles:

Tier 1: Word Heavyweight Championship
Tier 2: United States Championship
Tier 3: Television Championship
Tag Team: World Tag Team Championship
Novelty: Cruiserweight Championship

Possible PPVs: Starrcade, The Great American Bash, Slamboree and one other

In my opinion one of the big draws to WCW was fast action and high flying of the Cruiserweights. Plus it looks kind of ridiculous to have a guy the size of Mysterio with a strap when all a guy like Big Show has to do is get his hands on him once and it would be over. Give them their own strap and it looks a lot more legitimate. Plus, this division makes the dream of regular sized guys of being wrestler feel a lot more real.

ECW Hardcore [TV-MA]?
Rules: All matches are No Disqualification, No Holds Barred, Falls Count Anywhere
Titles:

Tier 1: World Hardcore Championship
Possible Tier 2 and 3: Cage (or Hell in a Cell) Championship, Last Man Standing Championship, 24/7 Hardcore Championship and Submission Championship
Tag Team: Tornado Tag Team Championship
Possible Novelty: Little People's Hardcore Championship

Possible PPVs: Hardcore Heaven, Anarchy Rulz, Barely Legal and one other

It seems to me that the biggest draw to ECW and the reason they had such a rabid fan loyalty was that there are quite a few people out there that want to see hardcore matches. I have seen that lately the WWE has been relaxing a little on their aversion to showing blood and on this show they would need to relax that quite a bit more and go back to the original rules of ECW, which is what made it great. Also, it seems to me that there has been quite a rise in the popularity of little people wrestling. It also seems to me that quite a few of them seem to be willing to do whatever it takes to make it in the industry. Why shouldn't the WWE be able to both capitalize on this and bring much more credibility to these wrestlers?

Other Possible PPVs: Night of Champions, Hell in a Cell, No Mercy, Backlash, Judgement Day, Vengeance, Money in the Bank, TLC, Sin, Uncensored, Hog Wild/Road Wild (Sturgis?), Bash at the Beach, Fall Brawl, Halloween Havoc, Mayhem

Alternatively each show could host its own pay-per-views using only its own talent and keeping the PPV profits for their own development and Corporate pay-per-views could be the only place where talent from all three shows would compete. Under this option Corporate should probably have Wrestlemania, the Royal Rumble, Night of Champions and Money in the Bank. The downside is that this would leave Monday Night Raw hosting SummerSlam, No Mercy, Backlash and Vengence or TLC. The upside, from Corporate viewpoint, is that there would be 16 pay-per-views per year.

Notes:
Use of the word Novelty in reference to certain types of wrestling is not meant as a slight it is simply acknowledging the fact that the WWE does not see them in the same light as the Heavyweight division.
All of these opinions are my own and I am not an expert so many of them may be completely wrong.