50/34 paired with an 11-28 cassette works well for me on most climbs in Europe

http://www.gear-calculator.com/

That will answer all of your gearing questions.
Compatibility depends on which derailleur you have.

You will need to install a medium arm rear derailleur to cater for more teeth on the cassette. Having said that, the standard Dura Ace 9100 RD has a longer arm (medium) than its predecessors which Shimano introduced to enable a 30 tooth cassette to be used with it. I have three bikes (2 road, 1TT) that are all currently set up with compact 50/34 cranks, the 9100 RD and 32 tooth cassettes. I live in a hilly area and I have never regretted having that extra bit of gearing. You need to have the appropriate length chain and the B tension screw adjusted accordingly.

Depending on your rear derailleur a 32 will work. I've done it with an Ultegra Di2 derailleur (pretty easy) and a SRAM Red (more difficult). Or, you can get one of these for $18. They work great and I didn't need to increase the chain length when I used it.

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Kevin

http://kevinmetcalfe.dreamhosters.com
My Strava

If it's Ultegra 6800, I'd get a GS rear derailleur if you want to use a 32T sprocket.
Going from 36T to 34T on the small chainring gets you a smallest gear that's 34/36 = 94.44% of the size. Likewise going from 28T to 32T on the cassette gets your smallest gear down to 87.5%. Do both at the same time and you're down to 82.6% of the original gear ratio. Gearing calculations are as easy as that.

For comparison purposes here are the gear ratios for each smallest gear combination for the configurations you seem to be considering (smaller number is a smaller/easier gear):
36 front, 28 rear = 1.286
36 front, 32 rear = 1.125
34 front, 28 rear = 1.214
34 front, 32 rear = 1.063

So just going to 32 at the back gets you a much easier gear.
I've got a Ultegra 6800 on my road bike using 50/34 chainrings and I generally ride it with an 11-28 cassette. For a really tough sportive in the Alps last year (Marmotte), I replaced the rear derailleur with the medium cage version (that's the GS rather than stock SS version) and used a 11-32 cassette. I hardly used the 32T at all, but I was glad to know it was there if I needed it. I wouldn't hesitate to recommend that approach. You can always go back to a narrower range cassette whenever you like. I'd say try the bigger cassette first and if you need more after you've tried that, you can still swap the chainrings.

Thanks a lot for the replies. What is a GS derailleur?

SS = short cage
GS = medium cage

I think Shimano says you can't do this, but with a properly set up 6800 drivetrain (including a properly sized chain) you can run a 11x30t or 11x32t cassette with the SS derailleur. I do it all the time, never had a problem.

I've heard 30T is workable. 32T too?
Are you confident there's no chance of clashes regardless of cross chaining and using big/big and small/small combinations?

A 32 tooth cassette will work with a short cage rear derailleur if you adjust the B screw.

However, I always use a medium cage so I don't get sued.

Again, I do it all the time, and have raced (mass start bike races) on that setup. That said, I do my own work and keep my drivetrain in very good condition, and I know how to size a chain. Perhaps more importantly, I've been riding for 40+ years and racing for 32, so I know how to shift. I cannot possibly know your level of mechanical skill, or riding skill.

I have cross chained as high as 52x28 (second cog from the wheel with the 11x32 cassette) and been fine, although this is obviously not an ideal gear to ride in. I rarely go any lower than the 14 or 15 when in the small ring, but again, no problems.

If you're nervous at all, follow jimatbeyond's advice and just get the GS derailleur, although now you'll also need a longer chain, and of course you'll need to install and adjust a new rear derailleur.

Another option would be to get the 32t cassette and ride it with the regular SS derailleur, and "test" for yourself whether this is a viable setup for you. That's how I got to this point, I needed a lower gear for one specific event, assumed I'd need the GS, but then after riding a week with the SS derailleur (and deliberately trying to get it to fail) I never bothered with the GS. Just adjust the b-screw as jimatbeyond says.

Well this is my point really. I wouldn't recommend this option to others without making them well aware of the potential pitfalls. You're careful with your setup and haven't actually tried big/big with a 32 at the back, so while you've had no problems, plenty people possibly will. What I would do and what I'd suggest to others is not always the same.