The 28-135 was the first lens I thought of, too.
It's a good lens with a nice range of focal lengths for a "walk-around". So many have been sold as kit lenses on 40, 50 and 60Ds, it's quite common to find it at nice prices on the used market. I paid $250 for one a couple years ago, that was like new, included the lens hood, a 72mm B+W MRC UV filter (that I promptly removed), both caps and shipping. I sometimes see them on my local Craigslist for as little as $200 or $225.
It's the third copy of this lens I've used and they've been consistently good. It's an EF lens with fast, quiet, accurate USM focus; is close focusing; has IS; and is decent "mid-grade/gold stripe" build. I bought it as a backup to my 24-70 and to be able to put on one of backup cameras as a loaner, should someone assisting me need a camera and lens.
But I sometimes use it for other reasons. My usual kit for equestrian events is 300/4 IS (sometimes with 1.4X teleconverter), 70-200/2.8 IS, 24-70/2.8 and a Tokina 12-24 for the occasional wide shot. However, those lenses and a pair of 7Ds make for a fairly backpack. When I know I'm going to have to hike a lot and am confident I'll have good light, I'll sometimes leave the 24-70 and 70-200 in the car and just take the 28-135 instead. You might say it's standing in for two L-series lenses.
The 55-250 might be a better choice for you, if you need that much reach. It's an EF-S lens, and doesn't have USM focus, so is slower, noisier and more erratic. But it's got good image quality, and is reasonably compact. It seems a little better built than the 18-55 IS or 50/1.8, but still is fairly plasticky.
I'm not claiming the 28-135 is a match for the 24-70L or 24-105L... It's simply not built or sealed as well as the two L-series. It's ever so slightly less sharp at focal lengths they all share and, in particular, a wee bit soft all the way out at 135mm. But you'll have a pretty hard time spotting the differences unless you make really big prints from each. Not anywhere near as much difference in IQ as you might expect from a lens that costs between 3X and 6X more.
Below are some images made with the 28-135 at various focal lengths...


Lucinda & Cisco 6th Obstacle, 2011 ACTHA Ride for the Mustangs, Hossmoor Ranch
EF 28-135mm lens at 47mm and f7.1. EOS 7D at ISO 400, 1/1000 shutter speed. Handheld, avail. light. Ready to go. 2011 ACTHA Ride for the Mustangs, Hossmoor Ranch
EF 28-135mm lens at 100mm and f7.1. EOS 7D at ISO 400, 1/800 shutter speed. Handheld, avail. light. Good boy! 2011 ACTHA Ride for the Mustangs, Hossmoor Ranch
EF 28-135mm lens at 117mm and f7.1. EOS 7D at ISO 400, 1/800 shutter speed. Handheld, avail. light. I'm pretty happy when I can count individual hairs and eyelashes and see every stitch in a horse's bridle.
Approaching Obstacle 6 2011 ACTHA Ride for the Mustangs, Hossmoor Ranch
EF 28-135mm lens at 135mm and f7.1. EOS 7D at ISO 400, 1/800 shutter speed. Handheld, avail. light. This last image is not so great, I'm not wild about the pose or backdrop. But it is shot at 135mm and you can see a bit of loss of fine detail in the enlargement, to see how this lens performs "at it's worst".
Some will tell you that a 24-whatever or 28-whatever lens is "not good" on a crop camera. They'll tell you that you "need" to buy a 17-whatever. Well, I disagree. I really like both 24-70 and 28-135 that I use. Wouldn't mind the 24-105 either. It's a convenient and versatile range of focal lengths for me. Note that I pair up with a 12-24mm ultrawide (there are a number of UWA possible) that complements either of the walk-around zooms quite well.
28-135mm is far from junk... In fact IMO it's one of the best deals in Canon lenses, particularly when bought lightly used. No other lens gives similar range of focal lengths and this combo of features, as well as decent build quality, focus performance and image quality, for so little money. It's sort of the Rodney Dangerfield of Canon lenses... it gets no respect!