You can hide the other dots by masking them from TeX's token scanner with { }, i.e.:
\includegraphics{{plot_a0.4_b0.6}.pdf}
works fine.
Note that the extension can also be dropped, then a list of default extensions is used. See the graphicx manual for more information.
If you want to do this, you need to double group the filename, which makes three together with the one for the arguments:
\includegraphics{{{plot_a0.4_b0.6}}}
The order of preference when files with the same name and different extensions is
.png .pdf .jpg .mps .jpeg .jbig2 .jb2 .PNG .PDF .JPG .JPEG .JBIG2 .JB2
which is stored in the macro \Gin@extensions. So if you have both image.png and image.pdf, pdflatex will load the former.
If you are mixing case in extensions, then
\DeclareGraphicsExtensions{%
.png,.PNG,%
.pdf,.PDF,%
.jpg,.mps,.jpeg,.jbig2,.jb2,.JPG,.JPEG,.JBIG2,.JB2}
will ensure that PNG are always preferred over PDF files. For the final version it will be sufficient to switch the two lines.
A handier way, suggested by Heiko Oberdiek, is to use the package grfext:
\usepackage{grfext}
\PrependGraphicsExtensions*{.png,.PNG}
that will have the same effect without the need to check in pdftex.def for the list of extensions.
If you want also automatic conversion, you can say
\usepackage{graphicx}
\usepackage{epstopdf}
\epstopdfDeclareGraphicsRule{.pdf}{png}{.png}{convert #1 \OutputFile}
\DeclareGraphicsExtensions{%
.png,.PNG,%
.pdf,.PDF,%
.jpg,.mps,.jpeg,.jbig2,.jb2,.JPG,.JPEG,.JBIG2,.JB2}
When image.pdf exists but not image.png, the file image-pdf-converted-to.png will be created and loaded in its place. Add the options you prefer between convert and #1 (for example -density 100 or something like that).
You need to call pdflatex with the --shell-escape option for this automatic conversion to work. Of course you'll comment out the \epstopdfDeclareGraphicsRule command for the final version, when only PDF files should be loaded (and switch the order of precedence in the lines below).
Best Answer
The LaTeX
graphics/graphicxpackage uses the first dot to find the extension. Packagegrffilechanges the algorithm to check for known extensions (optionmultidot, enabled by default):