I do like traditions and figurehead monarchies, As an actual form of government it certainly needs to end.
Similarly, I'd like noble titles to be brought back (around Europe), as officially recognized but without any actual privileges connected to them.

Most of the English-speaking Commonwealth nations confer honorary knighthood and peerages on people, i.e. OBE, as a high honor for people with major accomplishments. 

Absurd concept, imo. That you should be a fit leader, simply because your father or mother is a king or queen, is ridiculous to me.

That pretty much is what it boils down to. There are still some who believe you should get a title just because of your bloodline instead of earning it. But it's way less popular of an opinion than it was 100 years and longer ago. 

A head of state, even if their office is largely ceremonial, shouldn't be a hereditary office. Not only is the idea of power flowing from parent to child absurdly antiquated, but the taxpayers shouldn't be footing the bill to support a single wealthy family. Sure, there's tourism revenue and all, but you can still keep all the castles and jewels and guards and the rest of the historical elements and visual trappings without having an actual royal family. The ceremonial functions of head of state should be exercised by an elected officer.

Of course, on the flip side I think it's obvious at this point that republican governments with an executive president ought to consider demoting that office to a ceremonial one, thereby moving to a parliamentary system. We've had more than a few recent examples of executive presidents exercising (or at least attempting to) dictatorial powers, because that's what always inevitably happens in republics with a full presidential system. Not that a parliamentary system is a surefire bet against authoritarianism, but the overwhelming majority of the world's stable, functional democracies are those with parliamentary systems, while the number of full presidential republics that haven't dealt with authoritarian heads of state at some point numbers precisely zero.

Power in government should be diffuse, and never concentrated into a single officer. History shows time and time and time again that having a head of state that exercises any substantial amount of power is just asking for trouble, because sooner or later there's going to be someone in that office that doesn't give a damn about freedom, rule of law, or checks and balances and will seek to expand his power so that he can do whatever he pleases with impunity.

Here's a couple of quotes to keep in mind about forms of government:

"Many forms of government have been tried, and will be tried in this world of sin and woe. No one pretends that democracy is perfect or all-wise. Indeed it has been said that democracy is the worst form of government except for all those other forms that have been tried from time to time.…"

-Winston Churchill, Nov. 11, 1947

"Well, Doctor, what have we got, a republic or a monarchy?"
“A republic, if you can keep it.”

-Benjamin Franklin replying to Elizabeth Willing Powel, Sept. 17, 1787