In article ,
U wrote:

So which chargers can I leave permanently attached to a battery?

What you want is something called a "float charger". It provides a
carefully-regulated charging voltage (typically in the 13.5 - 13.8
volt range), with a current limiter.

The word 'trickle charger' or 'shore power' comes to mind.

A trickle charger may, or may not regulate the charging voltage
carefully enough to allow it to be hooked up on a semi-permanent basis.

If the voltage is too low, the battery may not maintain a good charge
state, and may not recharge if you run it down partway.

If the voltage is too high, the battery will begin "gassing" - the
high voltage breaks down the water in the electrolyte into hydrogen
and oxygen gasses. If you don't replace the lost water (using
distilled or demineralized water) periodically, the electrolyte level
will fall below the top of the plates, and you'll lose charge capacity
and may very well damage the battery permanently.

How is that
different from my old Sears charger which does me good for many years
already (but I unhook it after a day at most!).

Standard battery chargers are often of a dual-voltage variety. They
fast-charge the battery at a high voltage (around 14.4 volts) until
it's mostly charged, and then switch to a lower trickle-charge voltage
(13.8 or so) to finish the charging without excessive loss of
electrolyte.

Unless they're designed for long-term float charging use (careful
voltage regulation, with some amount of temperature-based adjustment
of the float voltage), leaving a charger of this sort hooked up on a
long-term basis can still result in some loss of electrolyte.

--
Dave Platt AE6EO
Hosting the Jade Warrior home page: http://www.radagast.org/jade-warrior
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