For full path names of changed files:

git log --name-only

For full path names and status of changed files:

git log --name-status

For abbreviated pathnames and a diffstat of changed files:

git log --stat

There are a lot more options. Check out the documentation.

This lets Git generate the patches for each log entry:

git log -p -- <filename>

-p in git generates patch text

See git help log for more options — it can actually do a lot of nice things. :)

To get just the diff for a specific commit, use

git show <revision> -- <filename>

or specify any other revision by identifier.

To browse the changes visually:

gitk -- <filename>

To see changes visually without leaving the console, run:

git blame-log <filename>

However, first ensure blame-log command exists, by at least once running:

# Virables: raw=unchanged-line, c=clean, B=Buffer,
git config --global alias.blame-log "! cd -- \"\${GIT_PREFIX:-.}\" && \
( if git grep -qI \".\" \"\$1\"; then \
    git log --oneline --color=always -L 1,\${2:-}:\"\$1\" | awk ' \
    { s=\$0; gsub(/\\033\\[[0-9;]*[mK]/, \"\", s) } \
    s~/^(diff|---|\\+\\+\+)/{next} \
    s~/^@@/{l=1;p=9;bi=0;cm=0;cp=0;next} s!~/^[-+ ]/{print;l=1;p=9;bi=0;cm=0;cp=0;next} \
    /^ /{ cm=0;cp=0; if(p<3){print;p++}else{b[bi%3]=\$0; bl[bi%3]=l; bi++} l++; next } \
    { if(p>=3){ n=(bi<3?bi:3); st=(bi<3?0:bi%3); print \"\\033[36mLine \"(n?bl[st]:l)\":\\033[m\"; for(k=0;k<n;k++)print b[(st+k)%3] } \
      p=0; if(s~/^-/){cm++;if(cm<=12)print;else if(cm==13)print\"...\"} else{cp++;if(cp<=12)print;else if(cp==13)print\"...\";l++} }'; \
else \
    echo \"Detected binary file, hence not showing lines-changed.\"
    git log --oneline --color=always \"\$1\";
fi ) | less -RX #"

Note that blame-log is intentionally limited to showing few lines per change-range, for example, to skip package-lock.json faster.

I would recommend using a different format than the default. My usual choice is a summary with the graph, but a one-line summary alone usually does the trick.

Option 1: One-line summary with a graph

git log --pretty=format:'%h : %s' --graph > log.log

Results in:

* 2d3acf9 : ignore errors from SIGCHLD on trap
*   5e3ee11 : Merge branch 'master' of git://github.com/dustin/grit
|\
| * 420eac9 : Added a method for getting the current branch.
* | 30e367c : timeout code and tests
* | 5a09431 : add timeout protection to grit
* | e1193f8 : support for heads with slashes in them
|/
* d6016bc : require time for xmlschema

Option 2: One-line summary without a graph

git log --pretty=format:'%h was %an, %ar, message: %s' > log.log

Results in:

a6b444f was Scott Chacon, 5 days ago, message: dammit, this is the second time this has re
49d77f7 was Scott Chacon, 8 days ago, message: modified index to create refs/heads if it i
9764edd was Hans Engel, 11 days ago, message: Add diff-lcs dependency
e1ba1e3 was Hans Engel, 11 days ago, message: Add dependency for Open4
0f87b4d was Scott Chacon, 12 days ago, message: merged recent changes

You can find more formatting options in the documentation here.