If you value small size and weight, this is a great standard zoom for full frame

I've had several of these over the years as I always end up buying another one after a while! Let me tell you why I like them so much:
OK, so it isn't an L lens. It's not big, heavy or expensive - and it isn't an amazing optical performer wide-open, particularly at short and medium focal lengths. It doesn't have IS.
But, guess what? It's really, really good stopped down a bit. A good example gives super-sharp consistent results across the frame at 5.6 and 8, and even right into the corners, at all focal lengths. This is much better than the best examples of the cheapest Canon zooms (like the 28-105 4-5.6. 28-90, most 28-80s, 35-80 etc). There are in-camera optical corrections available with cameras from the last 10 years or so. These reduce fringing and vignetting with my 6D. With newer cameras, distortion will also be compensated for.
Things to be aware of (in no particular order):
1. The duocam construction is not very tough and play between the different components can develop easily with a mistreated one. 2. Not necessarily because of 1, there is significant optical performance variation amongst the lenses in circulation. 3. Filters will easily induce mechanical vignetting at or near 28mm - it would have been better if Canon had chosen a bigger filter mount - but the lens would have been less compact! 4. Optical distortion is higher than I'd like at 28mm. 5. The basic optical and mechanical designs of all versions of 28-105 3.5-4.5 are the same - the only important differences are that the Mk II versions and some later examples of the Mk I have 7 aperture blades rather than 5. 6. After a lot of use, the lubricant in the zoom ring wears or dries and zoom feels less damped. Creep is not normally a problem as it is for many heavier Canon zooms. 7. The USM AF motor (like L lenses have) is smooth, fast and quiet but does eventually tend to fail - like all AF motors. 
This lens is often compared to the 24-85 3.5-4.5 USM which cost a little more and had a shorter production run. That's also a very good lens indeed, and you may prefer its focal length range. But it's not as easy to find a good one of those cheaply, and the two I've had over the years have had slightly less good extreme corners than the 28-105. If you're a perfectionist (how many users of old zooms are perfectionists?), the 28-105 is a slightly better lens.
These lenses work fine on cropped sensors but it is on full frame that they really make sense.

Yes, this is one of a family of USM lenses designed as kit lenses for mid-range and semi-pro bodies that were respectable and relatively cheap. First one in the series I used was the 28-80 USM Mk I (later models were less good) with thr EOS 100/Elan. Made a great pairing, both lens and camera incredibly quiet in use, radically more so than anything else on the market at the time. The 28-105 first came out with the EOS 5/A2E, and the 24-85 with the APS EOS IX. It culminated in the 28-135 IS, launched with the EOS 3 - optically slightly the best of the series, and with 2 stop IS as a bonus. All had similar construction and performance. Their direct descendent was the 24-105 f4 L - upgraded in many ways, but clearly of similar design and construction.

Also in this range was the 35-135, launched with the EOS 10/10S, but I've never owned or used this one.

As you say, this range are all very capable stopped down a bit. They all have some distortion, particularly at the wide end, the 24-85 having the most, but modern cameras can largely correct that in-camera. The 28-105 and 24-85 are particularly compact for their range, and are decent options even now for travelling light.

Bought once a very clean used copy of that lens in its box for the obvious reason that I wanted a lighter and more compact general use zoom lens. I let it go after a while for lack of IS. Obviously couldn't get sharp shots when light started to go down and had to increase shutter speed and thus iso and end up with noisier images. But it had beautiful rendering and smooth clean creamy bokeh. Much more appealing than the ef 24-105 stm that I own now. It would find new life now mounted on a stabilised Eos R body. I'm actually having my eyes on a clean one for sale. But to get a stabilised Eos R body now is not an option, if ever. Unless Canon releases a cheaper stabilised Eos R.

It was my standard FF to-go zoomlens for so many years. In fact I already had it in the film days. Then I thought the digital little Ixus could do everything better. Until I got another crop DSLR and then later the 5D, which came with ANOTHER 28-105. So I have 2 now. This lens has always given me excellent results (sharpness, beautiful bokeh, focussing accuracy and speed) and I totally don't understand why it has such a bad reputation. An old friend who is also a pro landscaper (see the wonderful name www.imaginature.nl) had printed out these gorgeous poster size prints, hanging in his shop and that's why I bought this lens in the first place.

If you go to the Digital Picture you can compare this lens to the 24-105L for sharpness, you will get a few eye openers. The trick is to treat this lens as a 5,6 fixed aperture lens. The 24-105 is an F4 lens, so this is your F5,6 lens. Practically just as sharp and way lighter.

Currently I am using a 28-135 and that one is WAY heavier (and perhaps a tad sharper in the centre). Below a holiday shot with the BRILLIANT 5D+28-105 combo that can be bought for 200 bucks or so nowadays but still makes stunning images, even by todays standards. And 200 bucks means you actually *dare* to take your camera to the beach which I gladly did (including swimming and leaving the camera under a towel).

Bas Hamstra