I've run two Tough Mudders so far. Once with a four-person team, once with my 60 year old father (if he can do it, you can).
A team is by no means required, but it sure does make it a lot more fun. Even if your "team" is just you and one other person. Camaraderie and such. It also helps having someone there for support and to help push you to keep going.
Most of the obstacles can be completed solo, but there are a few where having someone else really helps (some of the higher walls, the log carry, etc). Even if you are running solo though, you can usually find others to help you out along the way. TM is not really as much a race as it is an experience, so most of the other runners are pretty friendly and won't mind helping you out even if you are not on their team.
I would really urge you to get at least one other person to run with you, if for no other reason than that it will be more fun.
To be honest, while some of the obstacles can be challenging, the hardest part for me was the 10-12 miles of running. After running several miles, to me encountering the next obstacle was a welcome break. As long as you have reasonable upper body strength (if you can hoist yourself over a wall) then you should be fine. All obstacles are moderately physically demanding, but not impossible hard for the weekend warrior.
As far as cardio, mine sucks. Before I ran TM, I had never run more than 3 miles in my entire life, yet I was able to run the entire 10-12 miles each time without having to stop and walk or stop to rest (other than to hydrate briefly on occasion). As I said before, having all the obstacles break up the running really helps, in my opinion. If you can run a 6 min mile and do a 5k without stopping, you can probably handle TM just fine. It will be challenging, and you will have to push yourself, but you should be able to handle it.
That said, I still recommend that you do some jogging in the months before TM.
On a slightly related note, my 60yo father went on to run in World's Toughest Mudder in NJ last fall. He was literally the oldest one there. It's like TM, but lasts for 24 hours, and you basically see how many times you can run the course before time runs out. He managed to do two laps through the course (20 miles) before stopping to take a nap. After his nap he discovered that he was no longer able to move, but if he can do the course twice without stopping, I think you can do it once.
