$ apt-cache search --names-only firmware
Code:
grub-firmware-qemu - GRUB firmware image for QEMU
alsa-firmware-loaders - ALSA software loaders for specific hardware
firmware-b43-installer - firmware installer for the b43 driver
firmware-b43legacy-installer - firmware installer for the b43legacy driver
isight-firmware-tools - tools for dealing with Apple iSight firmware
linux-wlan-ng-firmware - firmware files used by the linux-wlan-ng driver
prism2-usb-firmware-installer - firmware files for the prism2_usb kernel driver
dns323-firmware-tools - build and manipulate firmware images for a range of NAS devices
expeyes-firmware-dev - hardware & software framework for developing science experiments
firmware-linux-free - Binary firmware for various drivers in the Linux kernel
sigrok-firmware-fx2lafw - Firmware for Cypress FX2(LP) based logic analyzers
atmel-firmware - Firmware for Atmel at76c50x wireless networking chips.
bluez-firmware - Firmware for Bluetooth devices
dahdi-firmware-nonfree - DAHDI non-free firmware
firmware-crystalhd - Crystal HD Video Decoder (firmware)
firmware-adi - Binary firmware for Analog Devices Inc. DSL modem chips
firmware-atheros - Binary firmware for Atheros wireless cards
firmware-bnx2 - Binary firmware for Broadcom NetXtremeII
firmware-bnx2x - Binary firmware for Broadcom NetXtreme II 10Gb
firmware-brcm80211 - Binary firmware for Broadcom 802.11 wireless cards
firmware-intelwimax - Binary firmware for Intel WiMAX Connection
firmware-ipw2x00 - Binary firmware for Intel Pro Wireless 2100, 2200 and 2915
firmware-ivtv - Binary firmware for iTVC15-family MPEG codecs (ivtv and pvrusb2 drivers)
firmware-iwlwifi - Binary firmware for Intel Wireless cards
firmware-libertas - Binary firmware for Marvell Libertas 8xxx wireless cards
firmware-linux - Binary firmware for various drivers in the Linux kernel (meta-package)
firmware-linux-nonfree - Binary firmware for various drivers in the Linux kernel
firmware-myricom - Binary firmware for Myri-10G Ethernet adapters
firmware-netxen - Binary firmware for QLogic Intelligent Ethernet (3000 and 3100 Series)
firmware-qlogic - Binary firmware for QLogic IBA7220, QLA1xxx, ISP2xxx and SP2x2
firmware-ralink - Binary firmware for Ralink wireless cards
firmware-realtek - Binary firmware for Realtek wired and wireless network adapters
firmware-samsung - Binary firmware for Samsung MFC video codecs
firmware-ti-connectivity - Binary firmware for TI Connectivity wireless network adapters
libertas-firmware - Firmware for Marvell's libertas wireless chip series (dummy package)
midisport-firmware - Firmware loader for M-Audio's MidiSport devices
firmware-zd1211 - binary firmware for the zd1211rw wireless driver
zd1211-firmware - transitional dummy package for firmware-zd1211
Check dmesg for what firmware you tried, but failed to get.
$ dmesg | grep -i firm
$ dmesg | grep -i fail
Currently on jessie, but shouldn't have changed much between releases. If dmesg shows a specific file name, you could use apt-file to locate the exact package that you need.
$ apt-file find rtl8168e-3.fw
Code:
firmware-realtek: /lib/firmware/rtl_nic/rtl8168e-3.fw
$ sudo apt-get install firmware-realtek
For my current machine anyway.