How to write units? In a scientific article, should I write "3m", "3 m", "3 meters", or "3 [meters]" ? 
 A: There is a standard set of rules for writing units in the SI. NIST and Physics Today both have summaries of them.
Basically, every standard unit has a standard abbreviation, which you're supposed to use. Unit names are set in roman, not italic, type, to distinguish them from variables. That is, $3\,m$ would mean three times the quantity represented by the variable $m$, but $3\,{\rm m}$ means 3 meters. Be careful to avoid ambiguity with compound units. Astrophysicists used to write ${\rm km/s/Mpc}$ a lot for the units for Hubble's constant, but that's bad. Better to write ${\rm km/(s\ Mpc)}$, and even better is ${\rm km\ s^{-1}\ Mpc^{-1}}$. There's a lot more at those Web sites.
A: I'd say it depends on how well established the units are. Commonly used SI units like m, s, kg, eV, etc. can certainly be used without writing their full name. 
As far as the distance between vaule and unit is concerned I think it is common to use one space in between (as in 1 m; the space should be unbreakable). For combined units (like kg/m³) there is usually no space in between the units if there is a scale modification (like the k in kg) or a mathematical symbol (the / in kg/m³ or the ³ in m³). 
On the other hand if there is an ommited multiplication sign (as in kg*m/s) there is usually a little space in between which is smaller than the normal spacing in text.
For further info you can read here http://www.ece.ucdavis.edu/~jowens/commonerrors.html . Down at the bottom is a remark to units.
A: a small aside: In British English (as opposed to American English) a meter is a measuring device, a metre is a unit of length.  This will depend on which dictionary you're following!
