For what it's worth....
Those original fuses are probably the old ceramic types - a plastic/ceramic center with exposed copper "clip on" ends & fuse link - yes?
They are great for burning fingers, shorting if external things touch them, and melting or flaming as the end terminals corrode or lose tension.
(Those clever Italians used them in my 1970's Ducati - a V-twin motorcycle that never vibrates nor is exposed to harsh environments - the fuse box being under the seat behind the rear cylinder etc etc.... LOL! It didn't take long for me to replace them with glass fuses. And Suzuki switches. And a (Lucas!) RITA ignition....)
Whilst the 3AG glass fuses improved the old ceramics by at least 15 years, these days even the glasses are old hat. (Their fuse boxes only last about 30 years.)
The modern solution is the blade fuse - less prone to "cheap" manufacturing faults, and far better contact security.
As Ween said (along with his other spot-on writing), the fuses are to protect the wiring - not the load. (Load protection fused are part of the load - ie, in amplifiers, or part of a special distribution - eg 5A or 7.5A etc for meters/gauges.)
The fuse size should generally be about 1/3rd bigger than the load.
EG - 2 x 55W lights = 110W = 110W/12V = 9.1A.
9.1 x 4/3 = 12.2A - hence next size is 15A.
Hence the wire should handle 15A too...
A 10A fuse is probably too small. Apart from running at 90% of its capacity (and hence warmer), it doesn't leave much extra capacity for higher voltages and hence higher currents.
That's consideration #1.
Another issue is ratings and tolerance. What if a 55W bulb is actually 60W or 65W?
Then there is the specification itself....
A 12V 55W lamp is probably NOT 55W @ 12V, but more likely to be 55W @ 13.8V.... 13.8V being the common voltage used for 12V equipment ratings.
[ FYI: A 12V system is rarely 12V! It can be over 15V but usually not above a max of 14.4V (the max long-term voltage for a 12V lead-acid battery), or 13.8V (the long-term "float" voltage of a fully charged battery) or 12.6-12.8V or lower (the voltage of the battery itself; fully charged).
In fact a battery at 12V (resting/idle) is roughly 60%-70% discharged - too low for a cyclic car battery, and near the limit for a deep cycle battery. ]
110W @ 13.8V = 8A (7.87A)
110W @ 14.4V should be 7.6A, but since it's lights and hence "resistive", it probably means at current of 8.3A (ie: 14.4/13.8 higher... from P=VI (for V=13.8) and V=IR etc etc...)
So the "real" current is less than your 12V calc. But not by much. Worst case is say 20% from 14.4V compared to 12V (14.4/12 = 1.2 = 120%). So current variation also is 20% from 12V to 14.4V. (NOTE - for a resistive load! This also means 44% more power - ie P=VI = 1.2 x 1.2 VI = 1.44 VI.)
But still, a 10A fuse is regarded as too small for an 8A load.
And THINK about distribution.
As Ween wrote, you do not want one thing killing everything else!
Separate the circuits. Separate critical from non-critical. (Stereo not on cooling fan. Lights on their own. Etc.)
In fact a recent change for me has been the conversion of lights from fuses to circuit breakers. I've only blown a light fuse ONCE where its been critical - I didn't (yet) have the flasher circuit (hi-beam, aka "passing") on its own separately fused circuit - a switch fault blew the fuse and I had no headlights. That was a tight winding country road late at night with a posted 100 kph limit. I was doing 160kph.
But to have fuses for headlights? They blow and are dead until replaced? How stupid is that! A circuit breaker will probably reconnect in seconds - at least for a while - everything helps. (Mind you I run separate fuses/breakers to each beam. Plus a redundant circuit for the high-beam just in case!)
So why all the crap above about Amperage ratings? Ooops... In summary...
Add ~30% to your
current calcs for the minimum sized fuse.
That gives the extra margin for the fuse itself as well as for current-voltage variations (20% if 12V - 14.4V, but probably only 10% for "normal" 13.8V rated stuff), and manufacturing tolerance (for the fuses & the loads).
And then round up to the next available size - eg: 9A + 30% =~12A => 15A fuse.
Then check that your downstream wire handles 15A.
Simple!
Ramble: Funny how fusing seem so easy, yet I have mentioned some of the complications. Hence "design rules" (of thumb) like "add 30%" etc. (I didn't mention temperature, nor fuse time delays (I^2t = IxI x t(seconds) etc.)
The ideal fusing is ONE fuse at the start of each wire (to protect the wire) and then the loads/equipment with their own fuses (if needed).
But then we distribute the wiring - eg a big 80A fused cable into smaller fused cables etc etc.
But how many series or in-line fuses do we want from the power source? Each fuse is an extra resistance. (And we don't want the "master" fuse tripping instead of the downstream fuses... but that's another lesson!).