Periodic Table Trends

General
Atomic Size
Atomic size increases down the groups as more protons are added to the nucleus and higher electron energy levels are filled.
It decreases from left to right across the periods as the same electron energy level is filled and the larger nucleus pulls the electrons closer. (Electron shielding lowers Zeff less than increasing numbers of protons in the nucleus raises it)

Ionization Energy
Ionization Energy (IE) is the energy needed to remove an electron from an atom. It decreases with increasing atomic size because the further away from the nucleus the less Zeff.

Electronegativity
Electronegativity (EN) is the ability to attract electrons and naturally follows the same pattern as IE, however this pattern is broken with the noble gases which already have a stable electron configuration.

Groups
Group 1 (Alkali Metals)
-In their periods they have the lowest molar mass, the largest atomic size, and (thus) the lowest density.
-They only have 1 valence electron which is far from their relatively small nucleus, so their metallic bonds are relatively weak; as a result they're soft, and have low melting points.
-Low IEs make them quite reactive.

Group 2 (Alkaline Earth Metals)
-Two valence electrons and more positive charges in the nucleus lead to stronger metallic bonding; this means they're harder and have higher melting points than the group 1 metals.
-Despite their higher IE they still form +2 ions because their lattice energy is so high. (Except Be, its IE and small size only allowing it to forms covalent bonds.)
-Salts formed by ions of these elements are less soluble because of their high lattice energy.

General Properties From Group 3 Onwards
-Elements in periods containing transition and/or inner transition elements have higher IEs and smaller atomic sizes because of the greater number of protons in their nucleus.
-It is possible for these elements to lose only their p orbital valence electrons when reacting. This happens when the additional energy needed to remove the 2 s orbital valence electrons would make the energy needed for the reaction greater than that released. As a result, many of these elements can have multiple oxidation states.

Group 3
-Generally form covalent bonds but can also form ionic ones. While removing 3 electrons takes a considerable amount of energy, much energy is released when these highly charged ions form compounds, thus allowing the reaction to proceed.

Group 4
-Only Sn and Pb can form ionic compounds, however they rarely do..

Group 5
-Like period 3 they generally form covalent bonds but sometimes form ionic bonds, in this case by gaining electrons. Bi can exhist as a cation by losing only its p orbital valence electrons.

Group 6
-Form anions more readily than group 5 elements.

Group 7
-Very reactive, form anions very readily because they only need to gain 1 outer electron.
-Pure forms exhist as diatomic molecules whos melting and boiling points increase with increasing molecular weight and stronger dispersion forces going down the group.
-Reactivity decreases down the group as EN decreases.

Group 8 (Noble Gases)
-So called because they generally don't form bonds with other atoms/molecules, however they can react with elements that have very high ENs.

Diagonal Relationships
Moving down a group increases atomic size but moving right across a period decreases it. This means some elements diagonal to one another on the periodic table exhibit similar properties (eg. Li and Mg).

See also:
Periodic Table