There's mounting pressure on social networks to prove that they can be profitable. Their answer to the revenue problem seems to be "more ads".
I think Twitter in particular has a number of opportunities for making money that have nothing to do with advertising. Here are some tools and features that I would pay for (separately, or as a part of a pro package).
There are a number of companies offering analytics for Twitter users: Crowdbooster, Buffer, Hootsuite, TwitterCounter. These services are charging $9+/month so users can see their top tweets (by retweet and "impressions"), their most clicked links, and insights on notable followers. Having this information is helpful for businesses and users with a big follower base.
Yes, I would pay for this: the ability to log-in once (on the web) and manage multiple Twitter accounts. Currently "you can only be logged in to one Twitter account at a time, in the same browser" (Twitter). It's odd to me that Twitter would push users to TweetDeck, when they could offer this as a premium service.
Twitter: let me schedule my tweets! Based on the click-through rates on my links, recommend which times I should tweet (Crowdbooster and Buffer currently do this). When I compose a tweet, let me choose between "Post Now" and "Schedule".
Desk.com and TwitSpark both offer the ability for support staff to reply to tweet inquiries from a single corporate Twitter account. These conversations are threaded, and include information on which team member resolved the case. Give companies the ability to have multiple people use the same account, but with different logins so it's more secure.
When I went to register my first Twitter account on Oct. 29, 2008 @justinjackson was already taken (I chose @mijustin instead). It looks like the original user registered via text message, but hasn't done anything with it since. This account has been inactive for 4 years. I know there are lots of other accounts like this as well. I'd like to see usernames that have been inactive for over 3 years opened up to auction: let us buy these unused Twitter handles!
Once I've published a tweet, the only way to fix a typo is to delete the tweet, and re-post. This ruins the initial permalink, which I might have already linked to in other places. Let premium users edit their tweets.