I've pulled my heavily loaded, custom trailer to Sturgis and back 4 times. I've used it for many shorter trips and I once even picked up 5, 35x15x12.5 tires on my golfcart trailer (I don't have a golf cart, but I love that little tilt trailer for hauling the bike itself, the riding lawn mower, the ol' ladies quad and my snowmobile).
I've gone over some serious mountain passes and when I first setup my trailer, got a speeding ticket for going 80 mph, with the trailer in tow. Not recommended but I was testing the trailer out to figure out how to best load it and what speed limitations I might have.
I've even clipped a Deer with the trailer and while I nearly soiled myself... everything was just fine.

All that and more on my 2000 FLSTC w/88B (carb'd) and never had a problem.
As previously mentioned... takes a little bit to get used to width and stopping, while not a problem does take a bit more room for safety. Loading things is the biggest deal though. Having your trailer sway in a truck or car is nowhere near as unnerving as having it happen on your 2 wheeled bike.

Bearing buddies and a small grease pack in your trailer is a good idea too.

 

I've been pulling my Aluma since '03 and have well over 100K on it. '02 Ultra, 2012 Ultra, and now a 2016 TriGlide all with Stage I and Tru-Duals. Never really had a problem power-wise with this combination.

 

I have this trailer and also a Time Out camper that
I pull with no trouble at all

 

No disrespect to anyone, i ride a 15 SGS, but if i were to pull a trailer i'd get me a triumph rocket3 touring. it would pull the trailer and an Ultra.

 

Yeah, 150 ft lbs of torque would make a good tow bike.

 

We love our 2001 American Legend (no longer made)....

 

Yeah...that would pull it up Pikes Peak loaded with gravel, and you wouldn't know it was there. So, would a Cummings diesel... But...what bike best to get, wasn't the op's question.

 

15 CVO Limited Marlow Trailer

I've pulled this trailer to Jackson Hole, stayed in Driggs Idaho and up Beartooth Pass. This bike is a dream to pull. And as far as warranty is concerned it's dealer decision as my dealer installed the hitch and wired it.

 

I've pulled a aluma trailer for 2 years and then we wanted to get out of tent so we bought a time out deluxe camper trailer. We have pulled it 2 years and 1st years we went east to NC, last year we went to Colorado. I have a 2012 ultra limited and it pulled both trailers just fine. The problem with us is that it seems like we keep taking more stuff so I did a big upgrade over the winter and put a 120 in bike so I'm looking forward to pulling the camper this year, did we have to do it, no!!. I'm getting a lot of miles on it so I had it tore down and I was going to do a bolt on 110 kit but found that the rod pin had spun and was binding up. That is why I ended up with the 120.

 

This is what we pull now.