Flash carts for Game Boy Color

If you want to load the games from an SD card to your Game Boy, a few realistic and useful options exists. The most well known is Everdrive, where people seem to recommend the X5 as a budget option or X7 as the real deal, but it is also quite expensive. Than there is also ElCheapoSD, and a bunch of them from China. Other options seem to be discontinued or require some additional ingenuity.

TL;DR: If you just want to play some Game Boy games this is what I would do:

Get a Game Boy Advance (GBA, SP or SP AGS-101)
Get EZ-FLASH OMEGA
Optional IPS screen
Custom firmware on EZ-FLASH OMEGA , this will allow you to emulate multiple systems like Game Gear, Neo Geo Pocket, PC-Engine and many more (check the website)

This way you have access to all three generations games (GB, GBC, GBA), a bunch of mods (IPS, battery, shells...) and a nice form factor (GBA).

Custom Game Cartridge

Price:~ 30€ Features: Looks like a Everdrive X3 clone, but without the firmware updates Link

ElCheapoSD v2.2

Price: ~40€ Features:

Max ROM size: 8MByte
Max SAVE RAM size: 128KByte
Cheat engine not yet completed but verified with current hardware
Save states on most games ~90%
Tested working on GBA, SP, GBC, DMG, Pocket; save states tested on GBA, GBC, SP, DMG, Pocket
Supported mappers: MBC1, MBC2, MBC3, MBC5 ROM
No RTC in this hardware version
8mbytes total, 4mbytes available for ROM
No battery required
Tested with cards 2gb to 32gb SDHC

Link

EZ-FLASH Junior

Price: ~40€ Features:

GB/GBC game copy and play
Instant load the game
Real time clock
Fast reset to menu
Maximum game: 64Mbits
Maximum save: 1Mbits
Mapper supports:MBC1,MBC2,MBC3,MBC5
Support Gameboy, Gameboy Pocket, Gameboy Color, Gameboy Advance/SP, even with backlit mods and rechargeable batteries.
System on chip level recovery mode, prevent upgrade dead
Support FAT32 4–32GB SD card
Firmware and kernel both are upgradable
Replaceable battery design

Link

EverDrive-GB X3

Price: ~40€ Features:

Max ROM size: 8MByte
Max SAVE RAM size: 128KByte
GameGenie cheat codes
Soft reset to menu
Supported mappers: MBC1, MBC2, MBC3, MBC5
SDHC/SDXC support
Compatible with all systems which supports GB and GBC cartridges, including Super Game Boy
OS supports up to 1000 files per folder

Link Same as X5 but requires reboot in menu to save game progress stored in SRAM (Like Mega-X3 or ED64-V2.5)

EverDrive-GB X5

Price:~ 78€ Features:

Max ROM size: 8MByte
Max SAVE RAM size: 128KByte
GameGenie cheat codes
Soft reset to menu
Supported mappers: MBC1, MBC2, MBC3, MBC5
SDHC/SDXC support
Compatible with all systems which supports GB and GBC cartridges, including Super Game Boy
OS supports up to 1000 files per folder

Link Same as X7 minus save states, in-game menu and RTC

EverDrive-GB X7

Price:~ 113€ Features:

Max ROM size: 8MByte
Max SAVE RAM size: 128KByte
Save States function and In-Game menu function
Isolated RTC function; “Isolated” means that multiple games can use RTC without interference; each game will have own copy of time
GameGenie cheat codes
Soft reset to menu
Supported mappers: MBC1, MBC2, MBC3, MBC5
SDHC/SDXC support
Compatible with all systems which supports GB and GBC cartridges, including Super Game Boy
OS supports up to 1000 files per folder