Is there a minecraft mod which lets you store unlimited items?

There are several mods that allow for great storage in Minecraft, depending on the resources you want to use and what you mean by unlimited.

Applied Energistics, otherwise known as "AE" -- is the gold standard for storage mods. It creates 'computers' that can digitally store as many items as you have storage capacity. AE's downsides is that the newest version is designed to be more late-game, its crafting system is not as compact as it used to be, and you need some sort of power mod to use the system at all. AE does best for large numbers of various items, instead of huge numbers of a single item or small numbers of a lot of different ones. However thanks to storage buses, you can connect AE to other storage mods that outperform it in their specialties.

Ancient Warfare -- Has the Warehouse. This is a lot like a non-tech version of AE's storage system. Items are added to an inventory system which can store huge number of materials. Like AE the warehouse must be powered. Unlike AE, however, the required power system is included in the mod, and it can be connected to a waterwheel or windmill with only moderate effort. This mod is known for not playing well with others, however, so it lacks the excellent compatibility of AE.

Just A Better Barrel Mod (aka JABBA) -- there are several barrel mods, which are blocks that can store a large number of a single item (IE stacks of coblestone) JABBA is considered one of the best. It is easy to get into, and at max JABBA barrels can store 8128 stacks of a single material each.

Iron Chests -- allow the creation of larger and larger chests which are basically vanilla in function. The largest of these can hold 108 stacks of items, and combined with Inventory Tweaks makes it a great storage mod for someone who doesn't want to get into machines.

Storage Drawers -- Is an ascetically pleasing mod featuring multi-compartment barrels. Of particular note is the Compacting Drawer, which will automatically combine any item that can be into its most "compact" form (ie iron nuggets into iron bars and then into iron blocks as possible.) This mod has great interactivity with AE, and can allow you to save a lot of AE storage very quickly and easily.

Extra Utilities -- has the filing cabinet, which unlike all of the above, is a single block that will hold a large number of the same item that do not normally stack. (IE books of enchantment or a multitude of pickaxes.)

MineFactory Reload -- offers the Deep Storage Unit. This is essentially a barrel in that it can only store one type of item at a time. Of note, however, is that it can store 2 billion units of that item and is easily moved. Greg's mod has a similar item known as the Quantum Chest.

Sky factory

I can't remember the exact mod, but you should download the Feed The Beast modpack, it has a lot of mods and different stuff like that, it makes the game a whole lot funner and adds so many new features.