Of course, there is the argument that Tag Teams don't sell. Maybe this is true, but the blame for this should fall on the promotions rather than the art of Tag Team wrestling itself. After all, it wasn't too long ago that the first ever Tables, Ladders, and Chairs match and the surrounding three-way feud between the Dudleys, Edge & Christian, and The Hardy Boys was the high-point of an entire year of WWE action. I specifically remember getting together with friends to watch Summerslam in 2000 specifically to see the debut of the TLC match. The "no-sale" axiom may hold true in the realm of merchandising or mainstream media attention, but from a fan's perspective, Tag Team storytelling can make for must-watch shows at the level of singles competition.
There's also the thought that because Tag Teams are less marketable or noticable, that it's a poor use of talent that could otherwise be better leveraged. To this I call shenanigans, as the WWE and TNA consistently miss opportunities to leverage singles stars as is, and it's certainly not because they have a partner. In fact, Tag Teams can serve multiple purposes in building up and maintaining talent - it can provide a less demanding work environment for an injured star, it can take a star out of the spotlight to freshen them up (this could have worked wonders for John Cena at various points), it's a great means of debuting talent, and it can also be used as an unfortunate holding ground for talents that creative has nothing for (think R-Truth and Kofi Kingston at present). There's no shortage of reasons to utilize Tag Team wrestling, just like there's no shortage of ways to utilize the division.
If you look back at the history of WWE/World Tag Team Championship holders, it's a veritable who's who of stars (mixed in with a veritable who's who of "who's that?" questions, I admit). Bret Hart and Shawn Michaels, as the foremost examples, started out as Tag Team wrestlers. The same goes for eventual World Champions Edge, Christian, Booker T, Scott Steiner, JBL, and Jeff Hardy. Further, the early-2000s were filled with Tag Teams comprised of high-end WWE stars (The Rock and Sock Connection, The Unholy Alliance, The Brothers of Destruction, The Two Man Power Trip, etc, etc). Say what you will about this period of Tag Team wrestling, but it wasn't that long ago that WWE was using it as a primary storytelling tool.
Furthermore, Tag Teams have the unqiue built-in feature of providing a potentially great storyline via a break-up. While it's silly to create teams just to break them up, some very memorable moments and feuds have revolved around the split of a Tag Team. Shawn Michaels kicking Marty Jannetty through a window is the foremost example, but Edge and Christian also had a great feud that was built up over months after Edge won the King of the Ring, while Impact Wrestling turned their greatest Tag Team (Beer Money) into their greatest feud to date (Bobby Roode v. James Storm).
Sadly, the list of recent Tag Team Champions doesn't inspire confidence as to the current state of the division. Kofi Kingston is now a two-time "we don't have a storyline for you" Champion, Primo and Epico held the titles for three months and I can't even remember them having a feud, and most of the promising teams of recent memory had quick break-ups when they had no other teams to face (the Nexus/Corre teams, The Hart Dynasty, the NXT pseudo-teams, etc).
The WWE roster (and FCW) is brimming with talent not being utilized. With six hours of shows each week (I'm including Superstars and NXT), the WWE has ample time available to re-commit to and re-develop the Tag Team ranks. Maybe the introduction of AW as a Manager, the designation of Kofi/Truth, Co-Bro, and Ziggler/Swagger as "real" teams, and the call-up of D-Young/Titus are good signs. Maybe they can find a partner for JTG, McGillicutty, Slater, and others, to remind us that they exist, refresh their personalities, and give them another chance to connect with the WWE Universe.
As I see it, the Tag Team ranks could actually be competitive, with real storylines and a bevy of teams fighting for the straps. Upon just a quick perusal of the WWE and FCW rosters, I can list 9 ready-made teams I'd be interested in seeing compete if given a reason to care about their matches and stories: Kofi/Truth, Ziggler/Swagger, CoBro, Young/Titus, Primo/Epico, Hunico/Camacho, Reks/Hawkins, The Usos, and The Roundas. All of these teams have shown potential either in the ring or in terms of personality. Yes, that statement applies to varying degrees, and some of these teams are more or less on life support at present, but that could easily be recovered (there's only one way to go for them, and that's up). Additionally, there are a handful of formerly entertaining stars who are doing nothing and could be paired up in the interim or the long-term to keep them on TV: Big Show, Drew McIntyre, Ezekial Jackson, Heath Slater, Justin Gabriel, Tyson Kidd, Trent Barretta, Yoshi Tatsu, JTG, and most of all, Alex Riley, who is being maddeningly jobbed out after connecting with the fans just a few months ago in his feud with the Miz.
No, not everyone can be in a Tag Team, and if they were, not all of them would get on TV. With that said, we have 30 minutes of Raw being devoted to John Laurinaitis, a non-wrestling character, and another 15 devoted to recaps. Raw last night had two tag matches, but only one involved actual Tag Teams and it was a 6-man match; SmackDown last week had two tag matches but one was a no-contest with non-teams; Raw the previous week had two tag matches but neither involved actual teams; Extreme Rules didn't have a single tag match, giving it the same number as Wrestlemania (unless you include the pre-show or the Maria Menounos spectacle).
I think I've belabored my point by now - the WWE has 6 hours of weekly television plus Pay Per Views, at least a half-dozen teams with potential, and a dozen singles competitors with nothing to do. I've bought a Pay Per View just to see a tag match, and it wasn't all that long ago. Some of the biggest stars in WWE history started out as Tag Team wrestlers. I could go on, but I don't think I should even have to...the current Tag Team utilization is laughable, and it's an easy fix in bringing up the low end of WWE cards to more entertaining levels.