Let's think about this in terms of peak emission. Wien's displacement law tells us that the peak emission wavelength of a black body, $\lambda_{\text{max}}$, is inversely proportional to its temperature, $T$:
$$\lambda_{\text{max}}=\frac{b}{T}$$
where $b$ is Wien's displacement constant; $b\simeq2.9\times10^{-3}\text{ m K}$. Using this and some assumptions about temperature, we can determine the peak of a star's spectrum, given that most stars are well-approximated as black bodies. Here, we assume that $T$ is the star's effective temperature, and pick a temperature in the general range of each type. I'm going to use the Harvard spectral classification.
$$\begin{array}{|c|c|c|c|}
\hline \text{Star type} & \text{Color} & T (\text{K}) & \lambda_{\text{max}}(\text{nm})\\
\hline \text{O} & \text{blue} & 35,000 & 82.9\\
\hline \text{B} & \text{blue-white} & 20,000 & 145\\
\hline \text{A} & \text{white} & 8,000 & 363\\
\hline \text{F} & \text{yellow-white} & 7,000 & 414\\
\hline \text{G} & \text{yellow} & 5,500 & 527\\
\hline \text{K} & \text{orange} & 4,000 & 725\\
\hline \text{M} & \text{red} & 3,000 & 967\\
\hline
\end{array}$$
Next, we have to assume that the plants are somewhat like the ones found on Earth - they use the same compounds and processes to survive. Life on Earth is all that currently exists in our dataset, and it's all we have to work with before delving into too much speculation.
One important process is photosynthesis. There are a variety of photosynthetic pigments available. I was able to find a book chapter detailing many of them along with their key property here, the wavelength(s) of maximum absorption $\lambda_{\text{abs}}$. Here's a table of the relevant ones:
$$\begin{array}{|c|c|c|}
\hline \text{Pigment} & \lambda_{\text{abs}}(\text{nm}) & \text{Occurrence}\\
\hline \text{Chlorophyll a} & 435, 670\text{-6}80 & \text{Photosynthetic plants}\\
\hline \text{Chlorophyll b} & 480, 650 & \text{Higher plants; green algae}\\
\hline \text{Chlorophyll c} & 435, 645 & \text{Diatoms; brown algae}\\
\hline \text{Chlorophyll d} & 435, 740 & \text{Red algae}\\
\hline \text{Chlorobium chlorophyll} & 750, 760 & \text{Green bacteria}\\
\hline \text{Bacteriochlorophyll a} & 800, 850, 890 & \text{Purple bacteria; green bacteria}\\
\hline \text{Bacteriochlorophyll b} & 435, 740 & \text{Rhodopseudomonas (a purple bacterium)}\\
\hline \alpha\text{-Carotene} & 420, 440, 470 & \text{Leaves; red algae; green algae}\\
\hline \beta\text{-Carotene} & 425, 450, 480 & \text{Most other plants}\\
\hline \gamma\text{-Carotene} & 440, 460, 495 & \text{Green sulfur bacteria}\\
\hline \text{Luteol} & 425, 445, 475 & \text{Green leaves; green algae; red algae}\\
\hline \text{Violaxanthol} & 425, 450, 475 & \text{Leaves}\\
\hline \text{Fucoxanthal} & 425, 450, 475 & \text{Diatoms; brown algae}\\
\hline \text{Spirilloxanthal} & 464, 490, 524 & \text{Purple bacteria}\\
\hline \text{Phycoerythrins} & 490, 546, 576 & \text{Red algae; some blue-green algae}\\
\hline \text{Phycocyanins} & 618 & \text{Blue-green algae; some red algae}\\
\hline \text{Allophycocyanin} & 654 & \text{Blue-green algae; red algae}\\
\hline
\end{array}$$
The Sun's $\lambda_{\text{max},\odot}$ is in the neighborhood of $500\text{ nm}$, landing it smack in the middle of all these pigments - as would be expected. I have some immediate observations:
- Many pigments have favorable absorption in the $\sim420\text{-}500\text{ nm}$ range, near $\lambda_{\text{max},\odot}$.
- There are a couple other peaks, from $618\text{-}680\text{ nm}$, $740\text{-}760\text{ nm}$, and $800\text{-}890\text{ nm}$. These are mainly due to pigments used by certain types of bacteria.
It stands to reason that if $\lambda_{\text{max},\odot}$ was somewhere else, different pigments would dominate. So let's add a couple columns to our first table:
$$\begin{array}{|c|c|c|c|}
\hline \text{Star type} & \lambda_{\text{max}}(\text{nm}) & \text{Possible dominant pigments} & \text{Possible dominant plants}\\
\hline \text{O} & 82.9 & \text{?} & \text{Algae}\\
\hline \text{B} & 145 & \text{?} & \text{Algae}\\
\hline \text{A} & 363 & \text{Miscellaneous algal pigments} & \text{Green and brown algae; some red algae}\\
\hline \text{F} & 414 & \text{Chlorophylls} & \text{Higher plants; green, brown and red algae}\\
\hline \text{G} & 527 & \text{Chlorophylls} & \text{Higher plants; blue-green algae}\\
\hline \text{K} & 725 & \text{Bacteriochlorophylls} & \text{Purple bacteria; green bacteria; blue-green algae}\\
\hline \text{M} & 967 & \text{Bacteriochlorophylls} & \text{Purple bacteria; green bacteria}\\
\hline
\end{array}$$
I've stated that algae would be the most likely plants on planets orbiting O- and B- type stars. This has nothing to do with pigments; rather, it is because these stars are so short-lived that multicellular life would have a hard time developing there. In fact, age may impact the types of life you would see across the board. More massive stars have less time for higher life to develop and so probably won't lead to complicated, multicellular life.
I still have to agree, at least in part, with Ville Niemi's answer. It's clear that plenty of different pigments exist on Earth, and there's no reason to think we wouldn't see even others on an alien world around a different star. However, in drastic enough cases (especially with M-dwarfs and O and B stars), there likely would be major shifts in the dominant pigments. Perhaps new ones would develop, and I can't speculate on those. I can, though, tell you which ones would gain some slight advantages. So maybe view this answer as saying "Well, maybe [X, Y, Z]" rather than something definitive, especially given that I'm no expert.