Carry on luggage

You should be just fine with Rick's 21" bag. Many of the budget airlines will limit you to 1 carry on, and nothing else (like a backpack, etc.) And they'll limit you to 10 kg. or 22 lbs. maximum. It's easy to go over that weight.

Also keep in mind when buying roller luggage is that weight may also be limited.

The following is a bit dated, but gives you an idea as to which airline limits carry-on weight in addition to size:
http://flyingwithfish.boardingarea.com/2009/06/28/carry-on-weight-baggage-limit-chart-for-65-world-airlines/
Lufthansa, SAS and Swiss are among the mainline carriers with 8 kg weight limits. Of course the test is whether they enforce the weight limit or not.

And make sure you don't pack it so tight it bulges. The bag is officially 9" in depth but some airlines allow only 8".

You should check the airlines you plan to fly to make sure the bag fits. There are some where the bag will be too big.

Like MrsEB, we purchased bag check-in for upcoming flights on Ryanair and EasyJet . They might have passed the size and weight rules for carrying on, but we prefer to avoid the stress of potentially paying $$$ to check the bags at the gate. (AND no restrictions on carry-on liquids.)

Last May when we flew an AF leg (Airbus A321) from Florence to CDG, the gate agent put our RS 21" rolling carryons in the little metal sizing bin at the gate. Mine passed, but the wife had stuffed her outside pockets full of souvenirs. I moved some bulk from hers into mine, compressed them both and we each squeaked by for carry-on; i.e. the dimensions all worked for AirFrance as long as the expandable pockets weren't maxed out. Recently I have peeked online and noted that AirFrance and the other majors do have allowed dimensions larger than some of the other airlines out there. I'd check carefully each airline I intend to use.

The link provided by Edgar has errors. Specifically, for Lufthansa. It says Lufthansa's limits are 22″x 16″x 8″, but Lufthansa's own website says 55 x 40 x 23 cm, which is exactly, to the nearest 1/100th of an inch, 21.65" x 15.75" x 9.07". So 22" would fail the maximum length by 3/8" and 16" would fail the maximum width by 1/4". And the weight is listed as 18#, when it is really 17.6#. Now, If you go by the website's conversion, Lufthansa might cut you a break on the inches to cm conversion, but they don't have to.

That size should be OK with most airlines.

Note that on busy flights, you may have to check in your luggage if they think that they can't fit all onboard. This happens fairly often and you don't have any choice in the matter.

Your main issue is going to be weight. Scandanavian, Lufthansa etc have an 8 kg limit. Most others are 10 kg but Easyjet is unlimited. Thomson is 5 kg. Bags are regularly weighed. It is easy to go overweight. Handbags etc will have to fit inside the suitcase as some strictly enforce the one bag only policy.

Taking hand luggage only doesn't save much time at most airports and who wants to do laundry on holiday? Check in bags is the best way to go in Europe unless you are away for less than a week.

The convertible without wheels will fit the requirements. I use a Campmor Essential carry on bag. It's basically the same as Rick's bag (I used to use one of his) but weighs less (can pack a little more) and costs less.

As has been said, if you stuff a soft sided carry on, you have two potential problems. One, it becomes thicker than allowed or two, it's heavier than allowed.

I've flown Lufthansa and SAS with only a carry-on. I've seen gate staff walk through the area with a scale. Anyone whose bag seems packed too full gets weighed. Since they are obviously overweight, they have to check.

I always make sure my bag weighs in under 18 lbs. total before I leave home. It doesn't look oversize or overfilled and, so far, I've never been asked to weigh it at an airport - but I know I'd be fine if they did ask.

Checking on the way home, if I have to, isn't as big of deal. If the bag is lost, I've got more clothes/toiletries at home.

Not speaking about Rick's bag specifically (I had a bad experience with his convertible carry-on and choose to stick with other brands), but pay attention to the weight. I personally have never had a bag measured or had to fit it into one of those boxes they have at the gate, but I have had bags weighed at the gate. Try to make sure your bag weighs less than the 8-10kg limit set by most European airlines and try not to over-stuff it.