Question: I have a Canon 550D which I've been using for around a year now. I really love it and have learned a great deal with this and the 18 - 135mm kit lens. But now with experience I feel the need to get some better glass. I won't be buying a new body any time soon because I figure investing in some good glass is more important. 

As I have looked around, I see quite a few good used L lenses I can get in ebay for good bargain prices. But I know that the EF lenses don't have the same focal length in the cropped sensors. Is it a wise decision to buy these EF lenses or buy the cropped sensor alternatives?

I have the following lenses in mind that I am looking to buy down the line from the canon range over the next several months.

16-35mm f/2.8L, 24-70mm f/2.8L, 70-200 f/4L.

Are these apt choices for cropped sensors? I know most pros with FFs use these but I am a bit skeptic that they will serve the same purpose for me. If so what are the alternatives for this that have almost as good image quality?

Answer: 
The lineup of Canon crop (EF-S) lenses is not nearly as broad as the full-frame (EF) lenses.

* In the focal length of interest, some EF options give better image quality than the respective EF-S options.
* Additionally, some EF lenses offer features that are not available for EF-S lenses, such as weather sealing and stronger construction.
* (Not specific to the lenses you listed but) specialty lenses are only available in EF format, like fisheye and tilt-shift.

so yes, there are reasons to get full-frame lenses for a crop camera. For the specific lenses in question, @Joanne C's reasoning makes sense but today I personally think it is less important than it seemed to be in the past, as you have greater chances of upgrading your rebel to a higher crop body (7D class) than to a FF class. By the time you finally upgrade to FF class, you can sell your crop lenses for a good value.
I am going to keep it simple.

1. Many people do it. In fact, I have seen most people using APS-C camera with a mix of EF-S and EF lenses, and less people use **only** EF-S lenses.
2. Expensive lenses offers **excellent** image quality with the trade-off of being expensive, inflexible (usually a narrow zoom range, may cause more frequent lens changes) and heavy.

Do you want to spend more money, carry more weight, narrow your zoom range, **just to get better pixels**? This is entirely up to you, but **honestly** and generally, such lens is not a **must** by people not getting paid doing photography.